The Riemann-Lanczos equations in general relativity and their integrability

NASA Astrophysics Data System (ADS)

Dolan, P.; Gerber, A.

2008-06-01

The aim of this paper is to examine the Riemann-Lanczos equations and how they can be made integrable. They consist of a system of linear first-order partial differential equations that arise in general relativity, whereby the Riemann curvature tensor is generated by an unknown third-order tensor potential field called the Lanczos tensor. Our approach is based on the theory of jet bundles, where all field variables and all their partial derivatives of all relevant orders are treated as independent variables alongside the local manifold coordinates (xa) on the given space-time manifold M. This approach is adopted in (a) Cartan's method of exterior differential systems, (b) Vessiot's dual method using vector field systems, and (c) the Janet-Riquier theory of systems of partial differential equations. All three methods allow for the most general situations under which integrability conditions can be found. They give equivalent results, namely, that involutivity is always achieved at all generic points of the jet manifold M after a finite number of prolongations. Two alternative methods that appear in the general relativity literature to find integrability conditions for the Riemann-Lanczos equations generate new partial differential equations for the Lanczos potential that introduce a source term, which is nonlinear in the components of the Riemann tensor. We show that such sources do not occur when either of method (a), (b), or (c) are used.

A new (2+1) dimensional integrable evolution equation for an ion acoustic wave in a magnetized plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mukherjee, Abhik, E-mail: abhik.mukherjee@saha.ac.in; Janaki, M. S., E-mail: ms.janaki@saha.ac.in; Kundu, Anjan, E-mail: anjan.kundu@saha.ac.in

2015-07-15

A new, completely integrable, two dimensional evolution equation is derived for an ion acoustic wave propagating in a magnetized, collisionless plasma. The equation is a multidimensional generalization of a modulated wavepacket with weak transverse propagation, which has resemblance to nonlinear Schrödinger (NLS) equation and has a connection to Kadomtsev-Petviashvili equation through a constraint relation. Higher soliton solutions of the equation are derived through Hirota bilinearization procedure, and an exact lump solution is calculated exhibiting 2D structure. Some mathematical properties demonstrating the completely integrable nature of this equation are described. Modulational instability using nonlinear frequency correction is derived, and the correspondingmore » growth rate is calculated, which shows the directional asymmetry of the system. The discovery of this novel (2+1) dimensional integrable NLS type equation for a magnetized plasma should pave a new direction of research in the field.« less

Gauge-invariant flow equation

NASA Astrophysics Data System (ADS)

Wetterich, C.

2018-06-01

We propose a closed gauge-invariant functional flow equation for Yang-Mills theories and quantum gravity that only involves one macroscopic gauge field or metric. It is based on a projection on physical and gauge fluctuations. Deriving this equation from a functional integral we employ the freedom in the precise choice of the macroscopic field and the effective average action in order to realize a closed and simple form of the flow equation.

Solvability of a Nonlinear Integral Equation in Dynamical String Theory

NASA Astrophysics Data System (ADS)

Khachatryan, A. Kh.; Khachatryan, Kh. A.

2018-04-01

We investigate an integral equation of the convolution type with a cubic nonlinearity on the entire real line. This equation has a direct application in open-string field theory and in p-adic string theory and describes nonlocal interactions. We prove that there exists a one-parameter family of bounded monotonic solutions and calculate the limits of solutions constructed at infinity.

An integral equation method for calculating sound field diffracted by a rigid barrier on an impedance ground.

PubMed

Zhao, Sipei; Qiu, Xiaojun; Cheng, Jianchun

2015-09-01

This paper proposes a different method for calculating a sound field diffracted by a rigid barrier based on the integral equation method, where a virtual boundary is assumed above the rigid barrier to divide the whole space into two subspaces. Based on the Kirchhoff-Helmholtz equation, the sound field in each subspace is determined with the source inside and the boundary conditions on the surface, and then the diffracted sound field is obtained by using the continuation conditions on the virtual boundary. Simulations are carried out to verify the feasibility of the proposed method. Compared to the MacDonald method and other existing methods, the proposed method is a rigorous solution for whole space and is also much easier to understand.

Modelling of charged satellite motion in Earth's gravitational and magnetic fields

NASA Astrophysics Data System (ADS)

Abd El-Bar, S. E.; Abd El-Salam, F. A.

2018-05-01

In this work Lagrange's planetary equations for a charged satellite subjected to the Earth's gravitational and magnetic force fields are solved. The Earth's gravity, and magnetic and electric force components are obtained and expressed in terms of orbital elements. The variational equations of orbit with the considered model in Keplerian elements are derived. The solution of the problem in a fully analytical way is obtained. The temporal rate of changes of the orbital elements of the spacecraft are integrated via Lagrange's planetary equations and integrals of the normalized Keplerian motion obtained by Ahmed (Astron. J. 107(5):1900, 1994).

Analytical and numerical solutions for heat transfer and effective thermal conductivity of cracked media

NASA Astrophysics Data System (ADS)

Tran, A. B.; Vu, M. N.; Nguyen, S. T.; Dong, T. Q.; Le-Nguyen, K.

2018-02-01

This paper presents analytical solutions to heat transfer problems around a crack and derive an adaptive model for effective thermal conductivity of cracked materials based on singular integral equation approach. Potential solution of heat diffusion through two-dimensional cracked media, where crack filled by air behaves as insulator to heat flow, is obtained in a singular integral equation form. It is demonstrated that the temperature field can be described as a function of temperature and rate of heat flow on the boundary and the temperature jump across the cracks. Numerical resolution of this boundary integral equation allows determining heat conduction and effective thermal conductivity of cracked media. Moreover, writing this boundary integral equation for an infinite medium embedding a single crack under a far-field condition allows deriving the closed-form solution of temperature discontinuity on the crack and particularly the closed-form solution of temperature field around the crack. These formulas are then used to establish analytical effective medium estimates. Finally, the comparison between the developed numerical and analytical solutions allows developing an adaptive model for effective thermal conductivity of cracked media. This model takes into account both the interaction between cracks and the percolation threshold.

Oblique scattering from radially inhomogeneous dielectric cylinders: An exact Volterra integral equation formulation

NASA Astrophysics Data System (ADS)

Tsalamengas, John L.

2018-07-01

We study plane-wave electromagnetic scattering by radially and strongly inhomogeneous dielectric cylinders at oblique incidence. The method of analysis relies on an exact reformulation of the underlying field equations as a first-order 4 × 4 system of differential equations and on the ability to restate the associated initial-value problem in the form of a system of coupled linear Volterra integral equations of the second kind. The integral equations so derived are discretized via a sophisticated variant of the Nyström method. The proposed method yields results accurate up to machine precision without relying on approximations. Numerical results and case studies ably demonstrate the efficiency and high accuracy of the algorithms.

A new approach for electrical properties estimation using a global integral equation and improvements using high permittivity materials.

PubMed

Schmidt, Rita; Webb, Andrew

2016-01-01

Electrical Properties Tomography (EPT) using MRI is a technique that has been developed to provide a new contrast mechanism for in vivo imaging. Currently the most common method relies on the solution of the homogeneous Helmholtz equation, which has limitations in accurate estimation at tissue interfaces. A new method proposed in this work combines a Maxwell's integral equation representation of the problem, and the use of high permittivity materials (HPM) to control the RF field, in order to reconstruct the electrical properties image. The magnetic field is represented by an integral equation considering each point as a contrast source. This equation can be solved in an inverse method. In this study we use a reference simulation or scout scan of a uniform phantom to provide an initial estimate for the inverse solution, which allows the estimation of the complex permittivity within a single iteration. Incorporating two setups with and without the HPM improves the reconstructed result, especially with respect to the very low electric field in the center of the sample. Electromagnetic simulations of the brain were performed at 3T to generate the B1(+) field maps and reconstruct the electric properties images. The standard deviations of the relative permittivity and conductivity were within 14% and 18%, respectively for a volume consisting of white matter, gray matter and cerebellum. Copyright © 2015 Elsevier Inc. All rights reserved.

Transport equations for partially ionized reactive plasma in magnetic field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhdanov, V. M.; Stepanenko, A. A.

2016-06-08

Transport equations for partially ionized reactive plasma in magnetic field taking into account the internal degrees of freedom and electronic excitation of plasma particles are derived. As a starting point of analysis the kinetic equation with a binary collision operator written in the Wang-Chang and Uhlenbeck form and with a reactive collision integral allowing for arbitrary chemical reactions is used. The linearized variant of Grad’s moment method is applied to deduce the systems of moment equations for plasma and also full and reduced transport equations for plasma species nonequilibrium parameters.

Efficient Solution of Three-Dimensional Problems of Acoustic and Electromagnetic Scattering by Open Surfaces

NASA Technical Reports Server (NTRS)

Turc, Catalin; Anand, Akash; Bruno, Oscar; Chaubell, Julian

2011-01-01

We present a computational methodology (a novel Nystrom approach based on use of a non-overlapping patch technique and Chebyshev discretizations) for efficient solution of problems of acoustic and electromagnetic scattering by open surfaces. Our integral equation formulations (1) Incorporate, as ansatz, the singular nature of open-surface integral-equation solutions, and (2) For the Electric Field Integral Equation (EFIE), use analytical regularizes that effectively reduce the number of iterations required by iterative linear-algebra solution based on Krylov-subspace iterative solvers.

Nonlinear ion acoustic waves scattered by vortexes

NASA Astrophysics Data System (ADS)

Ohno, Yuji; Yoshida, Zensho

2016-09-01

The Kadomtsev-Petviashvili (KP) hierarchy is the archetype of infinite-dimensional integrable systems, which describes nonlinear ion acoustic waves in two-dimensional space. This remarkably ordered system resides on a singular submanifold (leaf) embedded in a larger phase space of more general ion acoustic waves (low-frequency electrostatic perturbations). The KP hierarchy is characterized not only by small amplitudes but also by irrotational (zero-vorticity) velocity fields. In fact, the KP equation is derived by eliminating vorticity at every order of the reductive perturbation. Here, we modify the scaling of the velocity field so as to introduce a vortex term. The newly derived system of equations consists of a generalized three-dimensional KP equation and a two-dimensional vortex equation. The former describes 'scattering' of vortex-free waves by ambient vortexes that are determined by the latter. We say that the vortexes are 'ambient' because they do not receive reciprocal reactions from the waves (i.e., the vortex equation is independent of the wave fields). This model describes a minimal departure from the integrable KP system. By the Painlevé test, we delineate how the vorticity term violates integrability, bringing about an essential three-dimensionality to the solutions. By numerical simulation, we show how the solitons are scattered by vortexes and become chaotic.

Resonance line polarization and the Hanle effect in optically thick media. I - Formulation for the two-level atom

NASA Astrophysics Data System (ADS)

Landi Degl'Innocenti, E.; Bommier, V.; Sahal-Brechot, S.

1990-08-01

A general formalism is presented to describe resonance line polarization for a two-level atom in an optically thick, three-dimensional medium embedded in an arbitrary varying magnetic field and irradiated by an arbitrary radiation field. The magnetic field is supposed sufficiently small to induce a Zeeman splitting much smaller than the typical line width. By neglecting atomic polarization in the lower level and stimulated emission, an integral equation is derived for the multipole moments of the density matrix of the upper level. This equation shows how the multipole moments at any assigned point of the medium are coupled to the multipole moments relative at a different point as a consequence of the propagation of polarized radiation between the two points. The equation also accounts for the effect of the magnetic field, described by a kernel locally connecting multipole moments of the same rank, and for the role of inelastic and elastic (or depolarizing) collisions. After having given its formal derivation for the general case, the integral equation is particularized to the one-dimensional and two-dimensional cases. For the one-dimensional case of a plane parallel atmosphere, neglecting both the magnetic field and depolarizing collisions, the equation here derived reduces to a previous one given by Rees (1978).

Bukhvostov-Lipatov model and quantum-classical duality

NASA Astrophysics Data System (ADS)

Bazhanov, Vladimir V.; Lukyanov, Sergei L.; Runov, Boris A.

2018-02-01

The Bukhvostov-Lipatov model is an exactly soluble model of two interacting Dirac fermions in 1 + 1 dimensions. The model describes weakly interacting instantons and anti-instantons in the O (3) non-linear sigma model. In our previous work [arxiv:arXiv:1607.04839] we have proposed an exact formula for the vacuum energy of the Bukhvostov-Lipatov model in terms of special solutions of the classical sinh-Gordon equation, which can be viewed as an example of a remarkable duality between integrable quantum field theories and integrable classical field theories in two dimensions. Here we present a complete derivation of this duality based on the classical inverse scattering transform method, traditional Bethe ansatz techniques and analytic theory of ordinary differential equations. In particular, we show that the Bethe ansatz equations defining the vacuum state of the quantum theory also define connection coefficients of an auxiliary linear problem for the classical sinh-Gordon equation. Moreover, we also present details of the derivation of the non-linear integral equations determining the vacuum energy and other spectral characteristics of the model in the case when the vacuum state is filled by 2-string solutions of the Bethe ansatz equations.

Additive noise-induced Turing transitions in spatial systems with application to neural fields and the Swift Hohenberg equation

NASA Astrophysics Data System (ADS)

Hutt, Axel; Longtin, Andre; Schimansky-Geier, Lutz

2008-05-01

This work studies the spatio-temporal dynamics of a generic integral-differential equation subject to additive random fluctuations. It introduces a combination of the stochastic center manifold approach for stochastic differential equations and the adiabatic elimination for Fokker-Planck equations, and studies analytically the systems’ stability near Turing bifurcations. In addition two types of fluctuation are studied, namely fluctuations uncorrelated in space and time, and global fluctuations, which are constant in space but uncorrelated in time. We show that the global fluctuations shift the Turing bifurcation threshold. This shift is proportional to the fluctuation variance. Applications to a neural field equation and the Swift-Hohenberg equation reveal the shift of the bifurcation to larger control parameters, which represents a stabilization of the system. All analytical results are confirmed by numerical simulations of the occurring mode equations and the full stochastic integral-differential equation. To gain some insight into experimental manifestations, the sum of uncorrelated and global additive fluctuations is studied numerically and the analytical results on global fluctuations are confirmed qualitatively.

Modified non-Abelian Toda field equations and twisted quasigraded Lie algebras

DOE Office of Scientific and Technical Information (OSTI.GOV)

Skrypnyk, T.

We construct a new family of quasigraded Lie algebras that admit the Kostant-Adler scheme. They coincide with special quasigraded deformations of twisted subalgebras of the loop algebras. Using them we obtain new hierarchies of integrable equations in partial derivatives which we call 'modified' non-Abelian Toda field hierarchies.

Interpreting the Coulomb-field approximation for generalized-Born electrostatics using boundary-integral equation theory.

PubMed

Bardhan, Jaydeep P

2008-10-14

The importance of molecular electrostatic interactions in aqueous solution has motivated extensive research into physical models and numerical methods for their estimation. The computational costs associated with simulations that include many explicit water molecules have driven the development of implicit-solvent models, with generalized-Born (GB) models among the most popular of these. In this paper, we analyze a boundary-integral equation interpretation for the Coulomb-field approximation (CFA), which plays a central role in most GB models. This interpretation offers new insights into the nature of the CFA, which traditionally has been assessed using only a single point charge in the solute. The boundary-integral interpretation of the CFA allows the use of multiple point charges, or even continuous charge distributions, leading naturally to methods that eliminate the interpolation inaccuracies associated with the Still equation. This approach, which we call boundary-integral-based electrostatic estimation by the CFA (BIBEE/CFA), is most accurate when the molecular charge distribution generates a smooth normal displacement field at the solute-solvent boundary, and CFA-based GB methods perform similarly. Conversely, both methods are least accurate for charge distributions that give rise to rapidly varying or highly localized normal displacement fields. Supporting this analysis are comparisons of the reaction-potential matrices calculated using GB methods and boundary-element-method (BEM) simulations. An approximation similar to BIBEE/CFA exhibits complementary behavior, with superior accuracy for charge distributions that generate rapidly varying normal fields and poorer accuracy for distributions that produce smooth fields. This approximation, BIBEE by preconditioning (BIBEE/P), essentially generates initial guesses for preconditioned Krylov-subspace iterative BEMs. Thus, iterative refinement of the BIBEE/P results recovers the BEM solution; excellent agreement is obtained in only a few iterations. The boundary-integral-equation framework may also provide a means to derive rigorous results explaining how the empirical correction terms in many modern GB models significantly improve accuracy despite their simple analytical forms.

Schwarzschild and linear potentials in Mannheim's model of conformal gravity

NASA Astrophysics Data System (ADS)

Phillips, Peter R.

2018-05-01

We study the equations of conformal gravity, as given by Mannheim, in the weak field limit, so that a linear approximation is adequate. Specialising to static fields with spherical symmetry, we obtain a second-order equation for one of the metric functions. We obtain the Green function for this equation, and represent the metric function in the form of integrals over the source. Near a compact source such as the Sun the solution no longer has a form that is compatible with observations. We conclude that a solution of Mannheim type (a Schwarzschild term plus a linear potential of galactic scale) cannot exist for these field equations.

Spinning particle and gauge theories as integrability conditions

NASA Astrophysics Data System (ADS)

Eisenberg, Yeshayahu

1992-02-01

Starting from a new four dimensional spinning point particle we obtain new representations of the standard four dimensional gauge field equations in terms of a generalized space (Minkowski + light cone). In terms of this new formulation we define linear systems whose integrability conditions imply the massive Dirac-Maxwell and the Yang-Mills equations. Research supported by the Rothschild Fellowship.

Generalized Case ``Van Kampen theory for electromagnetic oscillations in a magnetized plasma

NASA Astrophysics Data System (ADS)

Bairaktaris, F.; Hizanidis, K.; Ram, A. K.

2017-10-01

The Case-Van Kampen theory is set up to describe electrostatic oscillations in an unmagnetized plasma. Our generalization to electromagnetic oscillations in magnetized plasma is formulated in the relativistic position-momentum phase space of the particles. The relativistic Vlasov equation includes the ambient, homogeneous, magnetic field, and space-time dependent electromagnetic fields that satisfy Maxwell's equations. The standard linearization technique leads to an equation for the perturbed distribution function in terms of the electromagnetic fields. The eigenvalues and eigenfunctions are obtained from three integrals `` each integral being over two different components of the momentum vector. Results connecting phase velocity, frequency, and wave vector will be presented. Supported in part by the Hellenic National Programme on Controlled Thermonuclear Fusion associated with the EUROfusion Consortium, and by DoE Grant DE-FG02-91ER-54109.

Coupled NASTRAN/boundary element formulation for acoustic scattering

NASA Technical Reports Server (NTRS)

Everstine, Gordon C.; Henderson, Francis M.; Schuetz, Luise S.

1987-01-01

A coupled finite element/boundary element capability is described for calculating the sound pressure field scattered by an arbitrary submerged 3-D elastic structure. Structural and fluid impedances are calculated with no approximation other than discretization. The surface fluid pressures and normal velocities are first calculated by coupling a NASTRAN finite element model of the structure with a discretized form of the Helmholtz surface integral equation for the exterior field. Far field pressures are then evaluated from the surface solution using the Helmholtz exterior integral equation. The overall approach is illustrated and validated using a known analytic solution for scattering from submerged spherical shells.

A new aerodynamic integral equation based on an acoustic formula in the time domain

NASA Technical Reports Server (NTRS)

Farassat, F.

1984-01-01

An aerodynamic integral equation for bodies moving at transonic and supersonic speeds is presented. Based on a time-dependent acoustic formula for calculating the noise emanating from the outer portion of a propeller blade travelling at high speed (the Ffowcs Williams-Hawking formulation), the loading terms and a conventional thickness source terms are retained. Two surface and three line integrals are employed to solve an equation for the loading noise. The near-field term is regularized using the collapsing sphere approach to obtain semiconvergence on the blade surface. A singular integral equation is thereby derived for the unknown surface pressure, and is amenable to numerical solutions using Galerkin or collocation methods. The technique is useful for studying the nonuniform inflow to the propeller.

Spinor description of D = 5 massless low-spin gauge fields

NASA Astrophysics Data System (ADS)

Uvarov, D. V.

2016-07-01

Spinor description for the curvatures of D = 5 Yang-Mills, Rarita-Schwinger and gravitational fields is elaborated. Restrictions imposed on the curvature spinors by the dynamical equations and Bianchi identities are analyzed. In the absence of sources symmetric curvature spinors with 2s indices obey first-order equations that in the linearized limit reduce to Dirac-type equations for massless free fields. These equations allow for a higher-spin generalization similarly to 4d case. Their solution in the form of the integral over Lorentz-harmonic variables parametrizing coset manifold {SO}(1,4)/({SO}(1,1)× {ISO}(3)) isomorphic to the three-sphere is considered. Superparticle model that contains such Lorentz harmonics as dynamical variables, as well as harmonics parametrizing the two-sphere {SU}(2)/U(1) is proposed. The states in its spectrum are given by the functions on S 3 that upon integrating over the Lorentz harmonics reproduce on-shell symmetric curvature spinors for various supermultiplets of D = 5 space-time supersymmetry.

Inverse random source scattering for the Helmholtz equation in inhomogeneous media

NASA Astrophysics Data System (ADS)

Li, Ming; Chen, Chuchu; Li, Peijun

2018-01-01

This paper is concerned with an inverse random source scattering problem in an inhomogeneous background medium. The wave propagation is modeled by the stochastic Helmholtz equation with the source driven by additive white noise. The goal is to reconstruct the statistical properties of the random source such as the mean and variance from the boundary measurement of the radiated random wave field at multiple frequencies. Both the direct and inverse problems are considered. We show that the direct problem has a unique mild solution by a constructive proof. For the inverse problem, we derive Fredholm integral equations, which connect the boundary measurement of the radiated wave field with the unknown source function. A regularized block Kaczmarz method is developed to solve the ill-posed integral equations. Numerical experiments are included to demonstrate the effectiveness of the proposed method.

Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (4).

PubMed

Murase, Kenya

2016-01-01

Partial differential equations are often used in the field of medical physics. In this (final) issue, the methods for solving the partial differential equations were introduced, which include separation of variables, integral transform (Fourier and Fourier-sine transforms), Green's function, and series expansion methods. Some examples were also introduced, in which the integral transform and Green's function methods were applied to solving Pennes' bioheat transfer equation and the Fourier series expansion method was applied to Navier-Stokes equation for analyzing the wall shear stress in blood vessels.Finally, the author hopes that this series will be helpful for people who engage in medical physics.

Nonlinear response from transport theory and quantum field theory at finite temperature

NASA Astrophysics Data System (ADS)

Carrington, M. E.; Defu, Hou; Kobes, R.

2001-07-01

We study the nonlinear response in weakly coupled hot φ4 theory. We obtain an expression for a quadratic shear viscous response coefficient using two different formalisms: transport theory and response theory. The transport theory calculation is done by assuming a local equilibrium form for the distribution function and expanding in the gradient of the local four dimensional velocity field. By performing a Chapman-Enskog expansion on the Boltzmann equation we obtain a hierarchy of equations for the coefficients of the expanded distribution function. To do the response theory calculation we use Zubarev's techniques in nonequilibrium statistical mechanics to derive a generalized Kubo formula. Using this formula allows us to obtain the quadratic shear viscous response from the three-point retarded Green function of the viscous shear stress tensor. We use the closed time path formalism of real time finite temperature field theory to show that this three-point function can be calculated by writing it as an integral equation involving a four-point vertex. This four-point vertex can in turn be obtained from an integral equation which represents the resummation of an infinite series of ladder and extended-ladder diagrams. The connection between transport theory and response theory is made when we show that the integral equation for this four-point vertex has exactly the same form as the equation obtained from the Boltzmann equation for the coefficient of the quadratic term of the gradient expansion of the distribution function. We conclude that calculating the quadratic shear viscous response using transport theory and keeping terms that are quadratic in the gradient of the velocity field in the Chapman-Enskog expansion of the Boltzmann equation is equivalent to calculating the quadratic shear viscous response from response theory using the next-to-linear response Kubo formula, with a vertex given by an infinite resummation of ladder and extended-ladder diagrams.

Boundary regularized integral equation formulation of the Helmholtz equation in acoustics.

PubMed

Sun, Qiang; Klaseboer, Evert; Khoo, Boo-Cheong; Chan, Derek Y C

2015-01-01

A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated with calculation of the pressure field owing to radiating bodies in acoustic wave problems. This method facilitates the use of higher order surface elements to represent boundaries, resulting in a significant reduction in the problem size with improved precision. Problems with extreme geometric aspect ratios can also be handled without diminished precision. When combined with the CHIEF method, uniqueness of the solution of the exterior acoustic problem is assured without the need to solve hypersingular integrals.

Boundary regularized integral equation formulation of the Helmholtz equation in acoustics

PubMed Central

Sun, Qiang; Klaseboer, Evert; Khoo, Boo-Cheong; Chan, Derek Y. C.

2015-01-01

A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated with calculation of the pressure field owing to radiating bodies in acoustic wave problems. This method facilitates the use of higher order surface elements to represent boundaries, resulting in a significant reduction in the problem size with improved precision. Problems with extreme geometric aspect ratios can also be handled without diminished precision. When combined with the CHIEF method, uniqueness of the solution of the exterior acoustic problem is assured without the need to solve hypersingular integrals. PMID:26064591

High-order integral equation methods for problems of scattering by bumps and cavities on half-planes.

PubMed

Pérez-Arancibia, Carlos; Bruno, Oscar P

2014-08-01

This paper presents high-order integral equation methods for the evaluation of electromagnetic wave scattering by dielectric bumps and dielectric cavities on perfectly conducting or dielectric half-planes. In detail, the algorithms introduced in this paper apply to eight classical scattering problems, namely, scattering by a dielectric bump on a perfectly conducting or a dielectric half-plane, and scattering by a filled, overfilled, or void dielectric cavity on a perfectly conducting or a dielectric half-plane. In all cases field representations based on single-layer potentials for appropriately chosen Green functions are used. The numerical far fields and near fields exhibit excellent convergence as discretizations are refined-even at and around points where singular fields and infinite currents exist.

CALL FOR PAPERS: Special issue on Symmetries and Integrability of Difference Equations

NASA Astrophysics Data System (ADS)

Doliwa, Adam; Korhonen, Risto; Lafortune, Stephane

2006-10-01

This is a call for contributions to a special issue of Journal of Physics A: Mathematical and General entitled `Special issue on Symmetries and Integrability of Difference Equations' as featured at the SIDE VII meeting held during July 2006 in Melbourne (http://web.maths.unsw.edu.au/%7Eschief/side/side.html). Participants at that meeting, as well as other researchers working in the field of difference equations and discrete systems, are invited to submit a research paper to this issue. This meeting was the seventh of a series of biennial meetings devoted to the study of integrable difference equations and related topics. The notion of integrability was first introduced in the 19th century in the context of classical mechanics with the definition of Liouville integrability for Hamiltonian flows. Since then, several notions of integrability have been introduced for partial and ordinary differential equations. Closely related to integrability theory is the symmetry analysis of nonlinear evolution equations. Symmetry analysis takes advantage of the Lie group structure of a given equation to study its properties. Together, integrability theory and symmetry analysis provide the main method by which nonlinear evolution equations can be solved explicitly. Difference equations, just as differential equations, are important in numerous fields of science and have a wide variety of applications in such areas as: mathematical physics, computer visualization, numerical analysis, mathematical biology, economics, combinatorics, quantum field theory, etc. It is thus crucial to develop tools to study and solve difference equations. While the theory of symmetry and integrability for differential equations is now well-established, this is not yet the case for discrete equations. The situation has undergone impressive development in recent years and has affected a broad range of fields, including the theory of special functions, quantum integrable systems, numerical analysis, cellular automata, representations of quantum groups, symmetries of difference equations, discrete (difference) geometry, etc. Consequently, the aim of the special issue is to benefit from the occasion offered by the SIDE VII meeting to provide a collection of papers which represent the state-of-the-art knowledge for studying integrability and symmetry properties of difference equations. Scope of the special issue The special issue will feature papers which deal with themes that were covered by the SIDE VII Conference. These are •Integrability testing •Discrete geometry and visualization •Laurent phenomena and cluster algebras •Ultra-discrete systems •Random matrix theory •Algebraic-geometric approaches to integrability •Yang-Baxter equations •Quantum and classical integrable systems •Difference Galois theory Editorial policy •The subject of the paper should relate to the subject of the meeting. The Guest Editors will reserve the right to judge whether a contribution fits the scope of the topic of the special issue. •Contributions will be refereed and processed according to the usual procedure of the journal. •Conference papers may be based on already published work but should either •contain significant additional new results and/or insights or •give a survey of the present state of the art, a critical assessment of the present understanding of a topic, and a discussion of open problems. •Papers submitted by non-participants should be original and contain substantial new results. Guidelines for preparation of contributions • The deadline for contributed papers will be 15 January 2007. •There is a page limit of 16 printed pages (approximately 9600 words) per contribution. For submitted papers exceeding this length the Guest Editors reserve the right to request a reduction in length. Further advice on document preparation can be found at www.iop.org/Journals/jphysa •Contributions to the special issue should if possible be submitted electronically by web upload at www.iop.org/Journals/jphysa, or by email to jphysa@iop.org, quoting 'J. Phys. A Special Issue: SIDE VII'. Submissions should ideally be in standard LaTeX form; we are, however, able to accept most formats including Microsoft Word. Please see the website for further information on electronic submissions. •Authors unable to submit electronically may send hard-copy contributions to: Publishing Administrators, Journal of Physics A, Institute of Physics Publishing, Dirac House, Temple Back, Bristol BS1 6BE, UK, enclosing electronic code on floppy disk if available and quoting 'J. Phys. A Special Issue: SIDE VII'. • All contributions should be accompanied by a read-me file or covering letter giving the postal and email address for correspondence. The Publishing Office should be notified of any subsequent change of address. •The special issue will be published in the paper and online version of the journal. The corresponding author of each contribution will receive a complimentary copy of the issue.

Integrability in AdS/CFT correspondence: quasi-classical analysis

NASA Astrophysics Data System (ADS)

Gromov, Nikolay

2009-06-01

In this review, we consider a quasi-classical method applicable to integrable field theories which is based on a classical integrable structure—the algebraic curve. We apply it to the Green-Schwarz superstring on the AdS5 × S5 space. We show that the proposed method reproduces perfectly the earlier results obtained by expanding the string action for some simple classical solutions. The construction is explicitly covariant and is not based on a particular parameterization of the fields and as a result is free from ambiguities. On the other hand, the finite size corrections in some particularly important scaling limit are studied in this paper for a system of Bethe equations. For the general superalgebra \\su(N|K) , the result for the 1/L corrections is obtained. We find an integral equation which describes these corrections in a closed form. As an application, we consider the conjectured Beisert-Staudacher (BS) equations with the Hernandez-Lopez dressing factor where the finite size corrections should reproduce quasi-classical results around a general classical solution. Indeed, we show that our integral equation can be interpreted as a sum of all physical fluctuations and thus prove the complete one-loop consistency of the BS equations. We demonstrate that any local conserved charge (including the AdS energy) computed from the BS equations is indeed given at one loop by the sum of the charges of fluctuations with an exponential precision for large S5 angular momentum of the string. As an independent result, the BS equations in an \\su(2) sub-sector were derived from Zamolodchikovs's S-matrix. The paper is based on the author's PhD thesis.

The Radiated Field Generated by a Monopole Source in a Short, Rigid, Rectangular Duct. Degree awarded by George Washington Univ.

NASA Technical Reports Server (NTRS)

Lakota, Barbara Anne

1998-01-01

This thesis develops a method to model the acoustic field generated by a monopole source placed in a moving rectangular duct. The walls of the duct are assumed to be infinitesimally thin and the source is placed at the center of the duct. The total acoustic pressure is written in terms of the free-space pressure, or incident pressure, and the scattered pressure. The scattered pressure is the augmentation to the incident pressure due to the presence of the duct. It satisfies a homogeneous wave equation and is discontinuous across the duct walls. Utilizing an integral representation of the scattered pressure, a set of singular boundary integral equations governing the unknown jump in scattered pressure is derived. This equation is solved by the method of collocation after representing the jump in pressure as a double series of shape functions. The solution obtained is then substituted back into the integral representation to determine the scattered pressure, and the total acoustic pressure at any point in the field. A few examples are included to illustrate the influence of various geometric and kinematic parameters on the radiated sound field.

Integrability: mathematical methods for studying solitary waves theory

NASA Astrophysics Data System (ADS)

Wazwaz, Abdul-Majid

2014-03-01

In recent decades, substantial experimental research efforts have been devoted to linear and nonlinear physical phenomena. In particular, studies of integrable nonlinear equations in solitary waves theory have attracted intensive interest from mathematicians, with the principal goal of fostering the development of new methods, and physicists, who are seeking solutions that represent physical phenomena and to form a bridge between mathematical results and scientific structures. The aim for both groups is to build up our current understanding and facilitate future developments, develop more creative results and create new trends in the rapidly developing field of solitary waves. The notion of the integrability of certain partial differential equations occupies an important role in current and future trends, but a unified rigorous definition of the integrability of differential equations still does not exist. For example, an integrable model in the Painlevé sense may not be integrable in the Lax sense. The Painlevé sense indicates that the solution can be represented as a Laurent series in powers of some function that vanishes on an arbitrary surface with the possibility of truncating the Laurent series at finite powers of this function. The concept of Lax pairs introduces another meaning of the notion of integrability. The Lax pair formulates the integrability of nonlinear equation as the compatibility condition of two linear equations. However, it was shown by many researchers that the necessary integrability conditions are the existence of an infinite series of generalized symmetries or conservation laws for the given equation. The existence of multiple soliton solutions often indicates the integrability of the equation but other tests, such as the Painlevé test or the Lax pair, are necessary to confirm the integrability for any equation. In the context of completely integrable equations, studies are flourishing because these equations are able to describe the real features in a variety of vital areas in science, technology and engineering. In recognition of the importance of solitary waves theory and the underlying concept of integrable equations, a variety of powerful methods have been developed to carry out the required analysis. Examples of such methods which have been advanced are the inverse scattering method, the Hirota bilinear method, the simplified Hirota method, the Bäcklund transformation method, the Darboux transformation, the Pfaffian technique, the Painlevé analysis, the generalized symmetry method, the subsidiary ordinary differential equation method, the coupled amplitude-phase formulation, the sine-cosine method, the sech-tanh method, the mapping and deformation approach and many new other methods. The inverse scattering method, viewed as a nonlinear analogue of the Fourier transform method, is a powerful approach that demonstrates the existence of soliton solutions through intensive computations. At the center of the theory of integrable equations lies the bilinear forms and Hirota's direct method, which can be used to obtain soliton solutions by using exponentials. The Bäcklund transformation method is a useful invariant transformation that transforms one solution into another of a differential equation. The Darboux transformation method is a well known tool in the theory of integrable systems. It is believed that there is a connection between the Bäcklund transformation and the Darboux transformation, but it is as yet not known. Archetypes of integrable equations are the Korteweg-de Vries (KdV) equation, the modified KdV equation, the sine-Gordon equation, the Schrödinger equation, the Vakhnenko equation, the KdV6 equation, the Burgers equation, the fifth-order Lax equation and many others. These equations yield soliton solutions, multiple soliton solutions, breather solutions, quasi-periodic solutions, kink solutions, homo-clinic solutions and other solutions as well. The couplings of linear and nonlinear equations were recently discovered and subsequently received considerable attention. The concept of couplings forms a new direction for developing innovative construction methods. The recently obtained results in solitary waves theory highlight new approaches for additional creative ideas, promising further achievements and increased progress in this field. We are grateful to all of the authors who accepted our invitation to contribute to this comment section.

A functional equation for the specular reflection of rays.

PubMed

Le Bot, A

2002-10-01

This paper aims to generalize the "radiosity method" when applied to specular reflection. Within the field of thermics, the radiosity method is also called the "standard procedure." The integral equation for incident energy, which is usually derived for diffuse reflection, is replaced by a more appropriate functional equation. The latter is used to solve some specific problems and it is shown that all the classical features of specular reflection, for example, the existence of image sources, are embodied within this equation. This equation can be solved with the ray-tracing technique, despite the implemented mathematics being quite different. Several interesting features of the energy field are presented.

An integrated algorithm for hypersonic fluid-thermal-structural numerical simulation

NASA Astrophysics Data System (ADS)

Li, Jia-Wei; Wang, Jiang-Feng

2018-05-01

In this paper, a fluid-structural-thermal integrated method is presented based on finite volume method. A unified integral equations system is developed as the control equations for physical process of aero-heating and structural heat transfer. The whole physical field is discretized by using an up-wind finite volume method. To demonstrate its capability, the numerical simulation of Mach 6.47 flow over stainless steel cylinder shows a good agreement with measured values, and this method dynamically simulates the objective physical processes. Thus, the integrated algorithm proves to be efficient and reliable.

Aero-Optical Wavefront Propagation and Refractive Fluid Interfaces in Large-Reynolds-Number Compressible Turbulent Flows

DTIC Science & Technology

2005-12-31

are utilized with the eikonal equation of geometrical optics to propagate computationally the optical wavefronts in the near field. As long as the...aero-optical interactions. In terms of the refractive index field n and the optical path length (OPL), the eikonal equation is: |∇ (OPL)| = n , (9) (e.g...ray n(`, t) d` . (10) The OPL integral corresponds to inverting the eikonal equation 9. The physical distance along the beam propagation path for

Kinematic validation of a quasi-geostrophic model for the fast dynamics in the Earth's outer core

NASA Astrophysics Data System (ADS)

Maffei, S.; Jackson, A.

2017-09-01

We derive a quasi-geostrophic (QG) system of equations suitable for the description of the Earth's core dynamics on interannual to decadal timescales. Over these timescales, rotation is assumed to be the dominant force and fluid motions are strongly invariant along the direction parallel to the rotation axis. The diffusion-free, QG system derived here is similar to the one derived in Canet et al. but the projection of the governing equations on the equatorial disc is handled via vertical integration and mass conservation is applied to the velocity field. Here we carefully analyse the properties of the resulting equations and we validate them neglecting the action of the Lorentz force in the momentum equation. We derive a novel analytical solution describing the evolution of the magnetic field under these assumptions in the presence of a purely azimuthal flow and an alternative formulation that allows us to numerically solve the evolution equations with a finite element method. The excellent agreement we found with the analytical solution proves that numerical integration of the QG system is possible and that it preserves important physical properties of the magnetic field. Implementation of magnetic diffusion is also briefly considered.

Soliton solutions for ABS lattice equations: I. Cauchy matrix approach

NASA Astrophysics Data System (ADS)

Nijhoff, Frank; Atkinson, James; Hietarinta, Jarmo

2009-10-01

In recent years there have been new insights into the integrability of quadrilateral lattice equations, i.e. partial difference equations which are the natural discrete analogues of integrable partial differential equations in 1+1 dimensions. In the scalar (i.e. single-field) case, there now exist classification results by Adler, Bobenko and Suris (ABS) leading to some new examples in addition to the lattice equations 'of KdV type' that were known since the late 1970s and early 1980s. In this paper, we review the construction of soliton solutions for the KdV-type lattice equations and use those results to construct N-soliton solutions for all lattice equations in the ABS list except for the elliptic case of Q4, which is left to a separate treatment.

Accuracy of the Generalized Self-Consistent Method in Modelling the Elastic Behaviour of Periodic Composites

NASA Technical Reports Server (NTRS)

Walker, Kevin P.; Freed, Alan D.; Jordan, Eric H.

1993-01-01

Local stress and strain fields in the unit cell of an infinite, two-dimensional, periodic fibrous lattice have been determined by an integral equation approach. The effect of the fibres is assimilated to an infinite two-dimensional array of fictitious body forces in the matrix constituent phase of the unit cell. By subtracting a volume averaged strain polarization term from the integral equation we effectively embed a finite number of unit cells in a homogenized medium in which the overall stress and strain correspond to the volume averaged stress and strain of the constrained unit cell. This paper demonstrates that the zeroth term in the governing integral equation expansion, which embeds one unit cell in the homogenized medium, corresponds to the generalized self-consistent approximation. By comparing the zeroth term approximation with higher order approximations to the integral equation summation, both the accuracy of the generalized self-consistent composite model and the rate of convergence of the integral summation can be assessed. Two example composites are studied. For a tungsten/copper elastic fibrous composite the generalized self-consistent model is shown to provide accurate, effective, elastic moduli and local field representations. The local elastic transverse stress field within the representative volume element of the generalized self-consistent method is shown to be in error by much larger amounts for a composite with periodically distributed voids, but homogenization leads to a cancelling of errors, and the effective transverse Young's modulus of the voided composite is shown to be in error by only 23% at a void volume fraction of 75%.

Inverse scattering for an exterior Dirichlet program

NASA Technical Reports Server (NTRS)

Hariharan, S. I.

1981-01-01

Scattering due to a metallic cylinder which is in the field of a wire carrying a periodic current is considered. The location and shape of the cylinder is obtained with a far field measurement in between the wire and the cylinder. The same analysis is applicable in acoustics in the situation that the cylinder is a soft wall body and the wire is a line source. The associated direct problem in this situation is an exterior Dirichlet problem for the Helmholtz equation in two dimensions. An improved low frequency estimate for the solution of this problem using integral equation methods is presented. The far field measurements are related to the solutions of boundary integral equations in the low frequency situation. These solutions are expressed in terms of mapping function which maps the exterior of the unknown curve onto the exterior of a unit disk. The coefficients of the Laurent expansion of the conformal transformations are related to the far field coefficients. The first far field coefficient leads to the calculation of the distance between the source and the cylinder.

Lie-Hamilton systems on the plane: Properties, classification and applications

NASA Astrophysics Data System (ADS)

Ballesteros, A.; Blasco, A.; Herranz, F. J.; de Lucas, J.; Sardón, C.

2015-04-01

We study Lie-Hamilton systems on the plane, i.e. systems of first-order differential equations describing the integral curves of a t-dependent vector field taking values in a finite-dimensional real Lie algebra of planar Hamiltonian vector fields with respect to a Poisson structure. We start with the local classification of finite-dimensional real Lie algebras of vector fields on the plane obtained in González-López, Kamran, and Olver (1992) [23] and we interpret their results as a local classification of Lie systems. By determining which of these real Lie algebras consist of Hamiltonian vector fields relative to a Poisson structure, we provide the complete local classification of Lie-Hamilton systems on the plane. We present and study through our results new Lie-Hamilton systems of interest which are used to investigate relevant non-autonomous differential equations, e.g. we get explicit local diffeomorphisms between such systems. We also analyse biomathematical models, the Milne-Pinney equations, second-order Kummer-Schwarz equations, complex Riccati equations and Buchdahl equations.

A representation of solution of stochastic differential equations

NASA Astrophysics Data System (ADS)

Kim, Yoon Tae; Jeon, Jong Woo

2006-03-01

We prove that the logarithm of the formal power series, obtained from a stochastic differential equation, is an element in the closure of the Lie algebra generated by vector fields being coefficients of equations. By using this result, we obtain a representation of the solution of stochastic differential equations in terms of Lie brackets and iterated Stratonovich integrals in the algebra of formal power series.

Simulation electromagnetic scattering on bodies through integral equation and neural networks methods

NASA Astrophysics Data System (ADS)

Lvovich, I. Ya; Preobrazhenskiy, A. P.; Choporov, O. N.

2018-05-01

The paper deals with the issue of electromagnetic scattering on a perfectly conducting diffractive body of a complex shape. Performance calculation of the body scattering is carried out through the integral equation method. Fredholm equation of the second time was used for calculating electric current density. While solving the integral equation through the moments method, the authors have properly described the core singularity. The authors determined piecewise constant functions as basic functions. The chosen equation was solved through the moments method. Within the Kirchhoff integral approach it is possible to define the scattered electromagnetic field, in some way related to obtained electrical currents. The observation angles sector belongs to the area of the front hemisphere of the diffractive body. To improve characteristics of the diffractive body, the authors used a neural network. All the neurons contained a logsigmoid activation function and weighted sums as discriminant functions. The paper presents the matrix of weighting factors of the connectionist model, as well as the results of the optimized dimensions of the diffractive body. The paper also presents some basic steps in calculation technique of the diffractive bodies, based on the combination of integral equation and neural networks methods.

Interactions as intertwiners in 4D QFT

NASA Astrophysics Data System (ADS)

de Mello Koch, Robert; Ramgoolam, Sanjaye

2016-03-01

In a recent paper we showed that the correlators of free scalar field theory in four dimensions can be constructed from a two dimensional topological field theory based on so(4 , 2) equivariant maps (intertwiners). The free field result, along with recent results of Frenkel and Libine on equivariance properties of Feynman integrals, are developed further in this paper. We show that the coefficient of the log term in the 1-loop 4-point conformal integral is a projector in the tensor product of so(4 , 2) representations. We also show that the 1-loop 4-point integral can be written as a sum of four terms, each associated with the quantum equation of motion for one of the four external legs. The quantum equation of motion is shown to be related to equivariant maps involving indecomposable representations of so(4 , 2), a phenomenon which illuminates multiplet recombination. The harmonic expansion method for Feynman integrals is a powerful tool for arriving at these results. The generalization to other interactions and higher loops is discussed.

Reaction formulation for radiation and scattering from plates, corner reflectors and dielectric-coated cylinders

NASA Technical Reports Server (NTRS)

Wang, N. N.

1974-01-01

The reaction concept is employed to formulate an integral equation for radiation and scattering from plates, corner reflectors, and dielectric-coated conducting cylinders. The surface-current density on the conducting surface is expanded with subsectional bases. The dielectric layer is modeled with polarization currents radiating in free space. Maxwell's equation and the boundary conditions are employed to express the polarization-current distribution in terms of the surface-current density on the conducting surface. By enforcing reaction tests with an array of electric test sources, the moment method is employed to reduce the integral equation to a matrix equation. Inversion of the matrix equation yields the current distribution, and the scattered field is then obtained by integrating the current distribution. The theory, computer program and numerical results are presented for radiation and scattering from plates, corner reflectors, and dielectric-coated conducting cylinders.

Plane elasto-plastic analysis of v-notched plate under bending by boundary integral equation method. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Rzasnicki, W.

1973-01-01

A method of solution is presented, which, when applied to the elasto-plastic analysis of plates having a v-notch on one edge and subjected to pure bending, will produce stress and strain fields in much greater detail than presently available. Application of the boundary integral equation method results in two coupled Fredholm-type integral equations, subject to prescribed boundary conditions. These equations are replaced by a system of simultaneous algebraic equations and solved by a successive approximation method employing Prandtl-Reuss incremental plasticity relations. The method is first applied to number of elasto-static problems and the results compared with available solutions. Good agreement is obtained in all cases. The elasto-plastic analysis provides detailed stress and strain distributions for several cases of plates with various notch angles and notch depths. A strain hardening material is assumed and both plane strain and plane stress conditions are considered.

A Boundary Value Problem for Introductory Physics?

ERIC Educational Resources Information Center

Grundberg, Johan

2008-01-01

The Laplace equation has applications in several fields of physics, and problems involving this equation serve as paradigms for boundary value problems. In the case of the Laplace equation in a disc there is a well-known explicit formula for the solution: Poisson's integral. We show how one can derive this formula, and in addition two equivalent…

Electromagnetic Scattering from Arbitrarily Shaped Aperture Backed by Rectangular Cavity Recessed in Infinite Ground Plane

NASA Technical Reports Server (NTRS)

Cockrell, C. R.; Beck, Fred B.

1997-01-01

The electromagnetic scattering from an arbitrarily shaped aperture backed by a rectangular cavity recessed in an infinite ground plane is analyzed by the integral equation approach. In this approach, the problem is split into two parts: exterior and interior. The electromagnetic fields in the exterior part are obtained from an equivalent magnetic surface current density assumed to be flowing over the aperture and backed by an infinite ground plane. The electromagnetic fields in the interior part are obtained in terms of rectangular cavity modal expansion functions. The modal amplitudes of cavity modes are determined by enforcing the continuity of the electric field across the aperture. The integral equation with the aperture magnetic current density as an unknown is obtained by enforcing the continuity of magnetic fields across the aperture. The integral equation is then solved for the magnetic current density by the method of moments. The electromagnetic scattering properties of an aperture backed by a rectangular cavity are determined from the magnetic current density. Numerical results on the backscatter radar cross-section (RCS) patterns of rectangular apertures backed by rectangular cavities are compared with earlier published results. Also numerical results on the backscatter RCS patterns of a circular aperture backed by a rectangular cavity are presented.

The Reduction of Ducted Fan Engine Noise Via A Boundary Integral Equation Method

NASA Technical Reports Server (NTRS)

Tweed, J.; Dunn, M.

1997-01-01

The development of a Boundary Integral Equation Method (BIEM) for the prediction of ducted fan engine noise is discussed. The method is motivated by the need for an efficient and versatile computational tool to assist in parametric noise reduction studies. In this research, the work in reference 1 was extended to include passive noise control treatment on the duct interior. The BEM considers the scattering of incident sound generated by spinning point thrust dipoles in a uniform flow field by a thin cylindrical duct. The acoustic field is written as a superposition of spinning modes. Modal coefficients of acoustic pressure are calculated term by term. The BEM theoretical framework is based on Helmholtz potential theory. A boundary value problem is converted to a boundary integral equation formulation with unknown single and double layer densities on the duct wall. After solving for the unknown densities, the acoustic field is easily calculated. The main feature of the BIEM is the ability to compute any portion of the sound field without the need to compute the entire field. Other noise prediction methods such as CFD and Finite Element methods lack this property. Additional BIEM attributes include versatility, ease of use, rapid noise predictions, coupling of propagation and radiation both forward and aft, implementable on midrange personal computers, and valid over a wide range of frequencies.

An integral equation formulation for the diffraction from convex plates and polyhedra.

PubMed

Asheim, Andreas; Svensson, U Peter

2013-06-01

A formulation of the problem of scattering from obstacles with edges is presented. The formulation is based on decomposing the field into geometrical acoustics, first-order, and multiple-order edge diffraction components. An existing secondary-source model for edge diffraction from finite edges is extended to handle multiple diffraction of all orders. It is shown that the multiple-order diffraction component can be found via the solution to an integral equation formulated on pairs of edge points. This gives what can be called an edge source signal. In a subsequent step, this edge source signal is propagated to yield a multiple-order diffracted field, taking all diffraction orders into account. Numerical experiments demonstrate accurate response for frequencies down to 0 for thin plates and a cube. No problems with irregular frequencies, as happen with the Kirchhoff-Helmholtz integral equation, are observed for this formulation. For the axisymmetric scattering from a circular disc, a highly effective symmetric formulation results, and results agree with reference solutions across the entire frequency range.

The effect of air flow, panel curvature, and internal pressurization on field-incidence transmission loss. [acoustic propagation through aircraft fuselage

NASA Technical Reports Server (NTRS)

Koval, L. R.

1975-01-01

In the context of sound transmission through aircraft fuselage panels, equations for the field-incidence transmission loss (TL) of a single-walled panel are derived that include the effects of external air flow, panel curvature, and internal fuselage pressurization. These effects are incorporated into the classical equations for the TL of single panels, and the resulting double integral for field-incidence TL is numerically evaluated for a specific set of parameters.

Latent Heating Retrieval from TRMM Observations Using a Simplified Thermodynamic Model

NASA Technical Reports Server (NTRS)

Grecu, Mircea; Olson, William S.

2003-01-01

A procedure for the retrieval of hydrometeor latent heating from TRMM active and passive observations is presented. The procedure is based on current methods for estimating multiple-species hydrometeor profiles from TRMM observations. The species include: cloud water, cloud ice, rain, and graupel (or snow). A three-dimensional wind field is prescribed based on the retrieved hydrometeor profiles, and, assuming a steady-state, the sources and sinks in the hydrometeor conservation equations are determined. Then, the momentum and thermodynamic equations, in which the heating and cooling are derived from the hydrometeor sources and sinks, are integrated one step forward in time. The hydrometeor sources and sinks are reevaluated based on the new wind field, and the momentum and thermodynamic equations are integrated one more step. The reevalution-integration process is repeated until a steady state is reached. The procedure is tested using cloud model simulations. Cloud-model derived fields are used to synthesize TRMM observations, from which hydrometeor profiles are derived. The procedure is applied to the retrieved hydrometeor profiles, and the latent heating estimates are compared to the actual latent heating produced by the cloud model. Examples of procedure's applications to real TRMM data are also provided.

General Relativistic Theory of the VLBI Time Delay in the Gravitational Field of Moving Bodies

NASA Technical Reports Server (NTRS)

Kopeikin, Sergei

2003-01-01

The general relativistic theory of the gravitational VLBI experiment conducted on September 8, 2002 by Fomalont and Kopeikin is explained. Equations of radio waves (light) propagating from the quasar to the observer are integrated in the time-dependent gravitational field of the solar system by making use of either retarded or advanced solutions of the Einstein field equations. This mathematical technique separates explicitly the effects associated with the propagation of gravity from those associated with light in the integral expression for the relativistic VLBI time delay of light. We prove that the relativistic correction to the Shapiro time delay, discovered by Kopeikin (ApJ, 556, L1, 2001), changes sign if one retains direction of the light propagation but replaces the retarded for the advanced solution of the Einstein equations. Hence, this correction is associated with the propagation of gravity. The VLBI observation measured its speed, and that the retarded solution is the correct one.

Integrability from point symmetries in a family of cosmological Horndeski Lagrangians

NASA Astrophysics Data System (ADS)

Dimakis, N.; Giacomini, Alex; Paliathanasis, Andronikos

2017-07-01

For a family of Horndeski theories, formulated in terms of a generalized Galileon model, we study the integrability of the field equations in a Friedmann-Lemaître-Robertson-Walker space-time. We are interested in point transformations which leave invariant the field equations. Noether's theorem is applied to determine the conservation laws for a family of models that belong to the same general class. The cosmological scenarios with or without an extra perfect fluid with constant equation of state parameter are the two important cases of our study. The de Sitter universe and ideal gas solutions are derived by using the invariant functions of the symmetry generators as a demonstration of our result. Furthermore, we discuss the connection of the different models under conformal transformations while we show that when the Horndeski theory reduces to a canonical field the same holds for the conformal equivalent theory. Finally, we discuss how singular solutions provides nonsingular universes in a different frame and vice versa.

Particle localization, spinor two-valuedness, and Fermi quantization of tensor systems

NASA Technical Reports Server (NTRS)

Reifler, Frank; Morris, Randall

1994-01-01

Recent studies of particle localization shows that square-integrable positive energy bispinor fields in a Minkowski space-time cannot be physically distinguished from constrained tensor fields. In this paper we generalize this result by characterizing all classical tensor systems, which admit Fermi quantization, as those having unitary Lie-Poisson brackets. Examples include Euler's tensor equation for a rigid body and Dirac's equation in tensor form.

Duality and integrability: Electromagnetism, linearized gravity, and massless higher spin gauge fields as bi-Hamiltonian systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barnich, Glenn; Troessaert, Cedric

2009-04-15

In the reduced phase space of electromagnetism, the generator of duality rotations in the usual Poisson bracket is shown to generate Maxwell's equations in a second, much simpler Poisson bracket. This gives rise to a hierarchy of bi-Hamiltonian evolution equations in the standard way. The result can be extended to linearized Yang-Mills theory, linearized gravity, and massless higher spin gauge fields.

Generalized Legendre transformations and symmetries of the WDVV equations

NASA Astrophysics Data System (ADS)

Strachan, Ian A. B.; Stedman, Richard

2017-03-01

The Witten-Dijkgraaf-Verlinde-Verlinde (or WDVV) equations, as one would expect from an integrable system, has many symmetries, both continuous and discrete. One class—the so-called Legendre transformations—were introduced by Dubrovin. They are a discrete set of symmetries between the stronger concept of a Frobenius manifold, and are generated by certain flat vector fields. In this paper this construction is generalized to the case where the vector field (called here the Legendre field) is non-flat but satisfies a certain set of defining equations. One application of this more general theory is to generate the induced symmetry between almost-dual Frobenius manifolds whose underlying Frobenius manifolds are related by a Legendre transformation. This also provides a map between rational and trigonometric solutions of the WDVV equations.

Microscopic theory of linear light scattering from mesoscopic media and in near-field optics.

PubMed

Keller, Ole

2005-08-01

On the basis of quantum mechanical response theory a microscopic propagator theory of linear light scattering from mesoscopic systems is presented. The central integral equation problem is transferred to a matrix equation problem by discretization in transitions between pairs of (many-body) energy eigenstates. The local-field calculation which appears from this approach is valid down to the microscopic region. Previous theories based on the (macroscopic) dielectric constant concept make use of spatial (geometrical) discretization and cannot in general be trusted on the mesoscopic length scale. The present theory can be applied to light scattering studies in near-field optics. After a brief discussion of the macroscopic integral equation problem a microscopic potential description of the scattering process is established. In combination with the use of microscopic electromagnetic propagators the formalism allows one to make contact to the macroscopic theory of light scattering and to the spatial photon localization problem. The quantum structure of the microscopic conductivity response tensor enables one to establish a clear physical picture of the origin of local-field phenomena in mesoscopic and near-field optics. The Huygens scalar propagator formalism is revisited and its generality in microscopic physics pointed out.

On the mechanics of stress analysis of fiber-reinforced composites

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, V.G.

A general mathematical formulation is developed for the three-dimensional inclusion and inhomogeneity problems, which are practically important in many engineering applications such as fiber pullout of reinforced composites, load transfer behavior in the stiffened structural components, and material defects and impurities existing in engineering materials. First, the displacement field (Green's function) for an elastic solid subjected to various distributions of ring loading is derived in closed form using the Papkovich-Neuber displacement potentials and the Hankel transforms. The Green's functions are used to derive the displacement and stress fields due to a finite cylindrical inclusion of prescribed dilatational eigenstrain such asmore » thermal expansion caused by an internal heat source. Unlike an elliptical inclusion, the interior stress field in the cylindrical inclusion is not uniform. Next, the three-dimensional inhomogeneity problem of a cylindrical fiber embedded in an infinite matrix of different material properties is considered to study load transfer of a finite fiber to an elastic medium. By using the equivalent inclusion method, the fiber is modeled as an inclusion with distributed eigenstrains of unknown strength, and the inhomogeneity problem can be treated as an equivalent inclusion problem. The eigenstrains are determined to simulate the disturbance due to the existing fiber. The equivalency of elastic field between inhomogeneity and inclusion problems leads to a set of integral equations. To solve the integral equations, the inclusion domain is discretized into a finite number of sub-inclusions with uniform eigenstrains, and the integral equations are reduced to a set of algebraic equations. The distributions of eigenstrains, interior stress field and axial force along the fiber are presented for various fiber lengths and the ratio of material properties of the fiber relative to the matrix.« less

Principles of Discrete Time Mechanics

NASA Astrophysics Data System (ADS)

Jaroszkiewicz, George

2014-04-01

1. Introduction; 2. The physics of discreteness; 3. The road to calculus; 4. Temporal discretization; 5. Discrete time dynamics architecture; 6. Some models; 7. Classical cellular automata; 8. The action sum; 9. Worked examples; 10. Lee's approach to discrete time mechanics; 11. Elliptic billiards; 12. The construction of system functions; 13. The classical discrete time oscillator; 14. Type 2 temporal discretization; 15. Intermission; 16. Discrete time quantum mechanics; 17. The quantized discrete time oscillator; 18. Path integrals; 19. Quantum encoding; 20. Discrete time classical field equations; 21. The discrete time Schrodinger equation; 22. The discrete time Klein-Gordon equation; 23. The discrete time Dirac equation; 24. Discrete time Maxwell's equations; 25. The discrete time Skyrme model; 26. Discrete time quantum field theory; 27. Interacting discrete time scalar fields; 28. Space, time and gravitation; 29. Causality and observation; 30. Concluding remarks; Appendix A. Coherent states; Appendix B. The time-dependent oscillator; Appendix C. Quaternions; Appendix D. Quantum registers; References; Index.

Complete factorisation and analytic solutions of generalized Lotka-Volterra equations

NASA Astrophysics Data System (ADS)

Brenig, L.

1988-11-01

It is shown that many systems of nonlinear differential equations of interest in various fields are naturally imbedded in a new family of differential equations. This family is invariant under nonlinear transformations based on the concept of matrix power of a vector. Each equation belonging to that family can be brought into a factorized canonical form for which integrable cases can be easily identified and solutions can be found by quadratures.

The reduced basis method for the electric field integral equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fares, M., E-mail: fares@cerfacs.f; Hesthaven, J.S., E-mail: Jan_Hesthaven@Brown.ed; Maday, Y., E-mail: maday@ann.jussieu.f

We introduce the reduced basis method (RBM) as an efficient tool for parametrized scattering problems in computational electromagnetics for problems where field solutions are computed using a standard Boundary Element Method (BEM) for the parametrized electric field integral equation (EFIE). This combination enables an algorithmic cooperation which results in a two step procedure. The first step consists of a computationally intense assembling of the reduced basis, that needs to be effected only once. In the second step, we compute output functionals of the solution, such as the Radar Cross Section (RCS), independently of the dimension of the discretization space, formore » many different parameter values in a many-query context at very little cost. Parameters include the wavenumber, the angle of the incident plane wave and its polarization.« less

Computation of Separated and Unsteady Flows with One- and Two-Equation Turbulence Models

NASA Technical Reports Server (NTRS)

Ekaterinaris, John A.; Menter, Florian R.

1994-01-01

The ability of one- and two-equation turbulence models to predict unsteady separated flows over airfoils is evaluated. An implicit, factorized, upwind-biased numerical scheme is used for the integration of the compressible, Reynolds averaged Navier-Stokes equations. The turbulent eddy viscosity is obtained from the computed mean flowfield by integration of the turbulent field equations. The two-equation turbulence models are discretized in space with an upwind-biased, second order accurate total variation diminishing scheme. One and two-equation turbulence models are first tested for a separated airfoil flow at fixed angle of incidence. The same models are then applied to compute the unsteady flowfields about airfoils undergoing oscillatory motion at low subsonic Mach numbers. Experimental cases where the flow has been tripped at the leading edge and where natural transition was allowed to occur naturally are considered. The more recently developed field-equation turbulence models capture the physics of unsteady separated flow significantly better than the standard kappa-epsilon and kappa-omega models. However, certain differences in the hysteresis effects are obtained. For an untripped high-Reynolds-number flow, it was found necessary to take into account the leading edge transitional flow region in order to capture the correct physical mechanism that leads to dynamic stall.

Volume integrals associated with the inhomogeneous Helmholtz equation. Part 1: Ellipsoidal region

NASA Technical Reports Server (NTRS)

Fu, L. S.; Mura, T.

1983-01-01

Problems of wave phenomena in fields of acoustics, electromagnetics and elasticity are often reduced to an integration of the inhomogeneous Helmholtz equation. Results are presented for volume integrals associated with the Helmholtz operator, nabla(2) to alpha(2), for the case of an ellipsoidal region. By using appropriate Taylor series expansions and multinomial theorem, these volume integrals are obtained in series form for regions r 4' and r r', where r and r' are distances from the origin to the point of observation and source, respectively. Derivatives of these integrals are easily evaluated. When the wave number approaches zero, the results reduce directly to the potentials of variable densities.

Gauge and integrable theories in loop spaces

NASA Astrophysics Data System (ADS)

Ferreira, L. A.; Luchini, G.

2012-05-01

We propose an integral formulation of the equations of motion of a large class of field theories which leads in a quite natural and direct way to the construction of conservation laws. The approach is based on generalized non-abelian Stokes theorems for p-form connections, and its appropriate mathematical language is that of loop spaces. The equations of motion are written as the equality of a hyper-volume ordered integral to a hyper-surface ordered integral on the border of that hyper-volume. The approach applies to integrable field theories in (1+1) dimensions, Chern-Simons theories in (2+1) dimensions, and non-abelian gauge theories in (2+1) and (3+1) dimensions. The results presented in this paper are relevant for the understanding of global properties of those theories. As a special byproduct we solve a long standing problem in (3+1)-dimensional Yang-Mills theory, namely the construction of conserved charges, valid for any solution, which are invariant under arbitrary gauge transformations.

Spontaneous generation of singularities in paraxial optical fields.

PubMed

Aiello, Andrea

2016-04-01

In nonrelativistic quantum mechanics, the spontaneous generation of singularities in smooth and finite wave functions is a well understood phenomenon also occurring for free particles. We use the familiar analogy between the two-dimensional Schrödinger equation and the optical paraxial wave equation to define a new class of square-integrable paraxial optical fields that develop a spatial singularity in the focal point of a weakly focusing thin lens. These fields are characterized by a single real parameter whose value determines the nature of the singularity. This novel field enhancement mechanism may stimulate fruitful research for diverse technological and scientific applications.

Bifurcations of large networks of two-dimensional integrate and fire neurons.

PubMed

Nicola, Wilten; Campbell, Sue Ann

2013-08-01

Recently, a class of two-dimensional integrate and fire models has been used to faithfully model spiking neurons. This class includes the Izhikevich model, the adaptive exponential integrate and fire model, and the quartic integrate and fire model. The bifurcation types for the individual neurons have been thoroughly analyzed by Touboul (SIAM J Appl Math 68(4):1045-1079, 2008). However, when the models are coupled together to form networks, the networks can display bifurcations that an uncoupled oscillator cannot. For example, the networks can transition from firing with a constant rate to burst firing. This paper introduces a technique to reduce a full network of this class of neurons to a mean field model, in the form of a system of switching ordinary differential equations. The reduction uses population density methods and a quasi-steady state approximation to arrive at the mean field system. Reduced models are derived for networks with different topologies and different model neurons with biologically derived parameters. The mean field equations are able to qualitatively and quantitatively describe the bifurcations that the full networks display. Extensions and higher order approximations are discussed.

Alternative Derivations for the Poisson Integral Formula

ERIC Educational Resources Information Center

Chen, J. T.; Wu, C. S.

2006-01-01

Poisson integral formula is revisited. The kernel in the Poisson integral formula can be derived in a series form through the direct BEM free of the concept of image point by using the null-field integral equation in conjunction with the degenerate kernels. The degenerate kernels for the closed-form Green's function and the series form of Poisson…

Modeling of Graphene Planar Grating in the THz Range by the Method of Singular Integral Equations

NASA Astrophysics Data System (ADS)

Kaliberda, Mstislav E.; Lytvynenko, Leonid M.; Pogarsky, Sergey A.

2018-04-01

Diffraction of the H-polarized electromagnetic wave by the planar graphene grating in the THz range is considered. The scattering and absorption characteristics are studied. The scattered field is represented in the spectral domain via unknown spectral function. The mathematical model is based on the graphene surface impedance and the method of singular integral equations. The numerical solution is obtained by the Nystrom-type method of discrete singularities.

Lagrangian equations of motion of particles and photons in a Schwarzschild field

NASA Astrophysics Data System (ADS)

Ritus, V. I.

2015-11-01

The equations of motion of a particle in the gravitational field of a black hole are considered in a formulation that uses generalized coordinates, velocities, and accelerations and is convenient for finding the integrals of motion. The equations are rewritten in terms of the physical velocities and accelerations measured in the Schwarzschild frame by a stationary observer using proper local length and time standards. The attractive force due to the field and the centripetal acceleration of a particle is proportional to the particle kinetic energy m/\\sqrt{1 - v^2}, consistently with the fact that the particle kinetic energy and the photon energy \\hbarω in the field increase by the same factor compared with their values without a field. The attraction exerted on particles and photons by a gravitational field source is proportional to their kinetic energies. The particle trajectory in the ultrarelativistic limit v \\to 1 coincides with the photon trajectory.

The aerodynamics of propellers and rotors using an acoustic formulation in the time domain

NASA Technical Reports Server (NTRS)

Long, L. N.

1983-01-01

The aerodynamics of propellers and rotors is especially complicated because of the highly three-dimensional and compressible nature of the flow field. However, in linearized theory the problem is governed by the wave equation, and a numerically-efficient integral formulation can be derived. This reduces the problem from one in space to one over a surface. Many such formulations exist in the aeroacoustics literature, but these become singular integral equations if one naively tries to use them to predict surface pressures, i.e., for aerodynamics. The present paper illustrates how one must interpret these equations in order to obtain nonambiguous results. After the regularized form of the integral equation is derived, a method for solving it numerically is described. This preliminary computer code uses Legendre-Gaussian quadrature to solve the equation. Numerical results are compared to experimental results for ellipsoids, wings, and rotors, including effects due to lift. Compressibility and the farfield boundary conditions are satisfied automatically using this method.

Continual approach at T=0 in the mean field theory of incommensurate magnetic states in the frustrated Heisenberg ferromagnet with an easy axis anisotropy

NASA Astrophysics Data System (ADS)

Martynov, S. N.; Tugarinov, V. I.; Martynov, A. S.

2017-10-01

The algorithm of approximate solution was developed for the differential equation describing the anharmonical change of the spin orientation angle in the model of ferromagnet with the exchange competition between nearest and next nearest magnetic neighbors and the easy axis exchange anisotropy. The equation was obtained from the collinearity constraint on the discrete lattice. In the low anharmonicity approximation the equation is resulted to an autonomous form and is integrated in quadratures. The obvious dependence of the angle velocity and second derivative of angle from angle and initial condition was derived by expanding the first integral of the equation in the Taylor series in vicinity of initial condition. The ground state of the soliton solutions was calculated by a numerical minimization of the energy integral. The evaluation of the used approximation was made for a triple point of the phase diagram.

On the synchrotron radiation reaction in external magnetic field

NASA Astrophysics Data System (ADS)

Tursunov, Arman; Kološ, Martin

2017-12-01

We study the dynamics of point electric charges undergoing radiation reaction force due to synchrotron radiation in the presence of external uniform magnetic field. The radiation reaction force cannot be neglected in many physical situations and its presence modifies the equations of motion significantly. The exact form of the equation of motion known as the Lorentz-Dirac equation contains higher order Schott term which leads to the appearance of the runaway solutions. We demonstrate effective computational ways to avoid such unphysical solutions and perform numerical integration of the dynamical equations. We show that in the ultrarelativistic case the Schott term is small and does not have considerable effect to the trajectory of a particle. We compare results with the covariant Landau-Lifshitz equation which is the first iteration of the Lorentz-Dirac equation. Even though the Landau-Lifshitz equation is thought to be approximative solution, we show that in realistic scenarios both approaches lead to identical results.

What is integrability of discrete variational systems?

PubMed

Boll, Raphael; Petrera, Matteo; Suris, Yuri B

2014-02-08

We propose a notion of a pluri-Lagrangian problem, which should be understood as an analogue of multi-dimensional consistency for variational systems. This is a development along the line of research of discrete integrable Lagrangian systems initiated in 2009 by Lobb and Nijhoff, however, having its more remote roots in the theory of pluriharmonic functions, in the Z -invariant models of statistical mechanics and their quasiclassical limit, as well as in the theory of variational symmetries going back to Noether. A d -dimensional pluri-Lagrangian problem can be described as follows: given a d -form [Formula: see text] on an m -dimensional space (called multi-time, m > d ), whose coefficients depend on a sought-after function x of m independent variables (called field), find those fields x which deliver critical points to the action functionals [Formula: see text] for any d -dimensional manifold Σ in the multi-time. We derive the main building blocks of the multi-time Euler-Lagrange equations for a discrete pluri-Lagrangian problem with d =2, the so-called corner equations, and discuss the notion of consistency of the system of corner equations. We analyse the system of corner equations for a special class of three-point two-forms, corresponding to integrable quad-equations of the ABS list. This allows us to close a conceptual gap of the work by Lobb and Nijhoff by showing that the corresponding two-forms are closed not only on solutions of (non-variational) quad-equations, but also on general solutions of the corresponding corner equations. We also find an example of a pluri-Lagrangian system not coming from a multi-dimensionally consistent system of quad-equations.

What is integrability of discrete variational systems?

PubMed Central

Boll, Raphael; Petrera, Matteo; Suris, Yuri B.

2014-01-01

We propose a notion of a pluri-Lagrangian problem, which should be understood as an analogue of multi-dimensional consistency for variational systems. This is a development along the line of research of discrete integrable Lagrangian systems initiated in 2009 by Lobb and Nijhoff, however, having its more remote roots in the theory of pluriharmonic functions, in the Z-invariant models of statistical mechanics and their quasiclassical limit, as well as in the theory of variational symmetries going back to Noether. A d-dimensional pluri-Lagrangian problem can be described as follows: given a d-form on an m-dimensional space (called multi-time, m>d), whose coefficients depend on a sought-after function x of m independent variables (called field), find those fields x which deliver critical points to the action functionals for any d-dimensional manifold Σ in the multi-time. We derive the main building blocks of the multi-time Euler–Lagrange equations for a discrete pluri-Lagrangian problem with d=2, the so-called corner equations, and discuss the notion of consistency of the system of corner equations. We analyse the system of corner equations for a special class of three-point two-forms, corresponding to integrable quad-equations of the ABS list. This allows us to close a conceptual gap of the work by Lobb and Nijhoff by showing that the corresponding two-forms are closed not only on solutions of (non-variational) quad-equations, but also on general solutions of the corresponding corner equations. We also find an example of a pluri-Lagrangian system not coming from a multi-dimensionally consistent system of quad-equations. PMID:24511254

Deep learning beyond Lefschetz thimbles

NASA Astrophysics Data System (ADS)

Alexandru, Andrei; Bedaque, Paulo F.; Lamm, Henry; Lawrence, Scott

2017-11-01

The generalized thimble method to treat field theories with sign problems requires repeatedly solving the computationally expensive holomorphic flow equations. We present a machine learning technique to bypass this problem. The central idea is to obtain a few field configurations via the flow equations to train a feed-forward neural network. The trained network defines a new manifold of integration which reduces the sign problem and can be rapidly sampled. We present results for the 1 +1 dimensional Thirring model with Wilson fermions on sizable lattices. In addition to the gain in speed, the parametrization of the integration manifold we use avoids the "trapping" of Monte Carlo chains which plagues large-flow calculations, a considerable shortcoming of the previous attempts.

A rigorous solution of the Navier-Stokes equations for unsteady viscous flow at high Reynolds numbers around oscillating airfoils

NASA Technical Reports Server (NTRS)

Bratanow, T.; Aksu, H.; Spehert, T.

1975-01-01

A method based on the Navier-Stokes equations was developed for analyzing the unsteady incompressible viscous flow around oscillating airfoils at high Reynolds numbers. The Navier-Stokes equations have been integrated in their classical Helmholtz vorticity transport equation form, and the instantaneous velocity field at each time step was determined by the solution of Poisson's equation. A refined finite element was utilized to allow for a conformable solution of the stream function and its first space derivatives at the element interfaces. A corresponding set of accurate boundary conditions was applied; thus obtaining a rigorous solution for the velocity field. The details of the computational procedure and examples of computed results describing the unsteady flow characteristics around the airfoil are presented.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stoynov, Y.; Dineva, P.

The stress, magnetic and electric field analysis of multifunctional composites, weakened by impermeable cracks, is of fundamental importance for their structural integrity and reliable service performance. The aim is to study dynamic behavior of a plane of functionally graded magnetoelectroelastic composite with more than one crack. The coupled material properties vary exponentially in an arbitrary direction. The plane is subjected to anti-plane mechanical and in-plane electric and magnetic load. The boundary value problem described by the partial differential equations with variable coefficients is reduced to a non-hypersingular traction boundary integral equation based on the appropriate functional transform and frequency-dependent fundamentalmore » solution derived in a closed form by Radon transform. Software code based on the boundary integral equation method (BIEM) is developed, validated and inserted in numerical simulations. The obtained results show the sensitivity of the dynamic stress, magnetic and electric field concentration in the cracked plane to the type and characteristics of the dynamic load, to the location and cracks disposition, to the wave-crack-crack interactions and to the magnitude and direction of the material gradient.« less

PIV-based estimation of unsteady loads on a flat plate at high angle of attack using momentum equation approaches

NASA Astrophysics Data System (ADS)

Guissart, Amandine; Bernal, Luis; Dimitriadis, Gregorios; Terrapon, Vincent

2015-11-01

The direct measurement of loads with force balance can become challenging when the forces are small or when the body is moving. An alternative is the use of Particle Image Velocimetry (PIV) velocity fields to indirectly obtain the aerodynamic coefficients. This can be done by the use of control volume approaches which lead to the integration of velocities, and other fields deriving from them, on a contour surrounding the studied body and its supporting surface. This work exposes and discusses results obtained with two different methods: the direct use of the integral formulation of the Navier-Stokes equations and the so-called Noca's method. The latter is a reformulation of the integral Navier-Stokes equations in order to get rid of the pressure. Results obtained using the two methods are compared and the influence of different parameters is discussed. The methods are applied to PIV data obtained from water channel testing for the flow around a 16:1 plate. Two cases are considered: a static plate at high angle of attack and a large amplitude imposed pitching motion. Two-dimensional PIV velocity fields are used to compute the aerodynamic forces. Direct measurements of dynamic loads are also carried out in order to assess the quality of the indirectly calculated coefficients.

Role of nonlinear refraction in the generation of terahertz field pulses by light fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zabolotskii, A. A., E-mail: zabolotskii@iae.nsk.su

2013-07-15

The generation of microwave (terahertz) pulses without any envelope in a four-level quasi-resonant medium is considered. Two intense quasi-monochromatic laser fields lead to a partial upper-level population. Microwave field pulses cause the transition between these levels. For appropriately chosen scales, the evolution of the fields is shown to be described by the pseudo-spin evolution equations in a microwave field with the inclusion of nonlinear refraction caused by an adiabatic upper-level population. The evolution of terahertz field pulses is described outside the scope of the slow-envelope approximation. When a number of standard approximations are taken into account, this system of equationsmore » is shown to be equivalent to an integrable version of the generalized reduced Maxwell-Bloch equations or to the generalized three-wave mixing equations. The soliton solution found by the inverse scattering transform method is used as an example to show that nonlinear refraction leads to a strong compression of the microwave (terahertz) field soliton.« less

Numerical calculations of velocity and pressure distribution around oscillating airfoils

NASA Technical Reports Server (NTRS)

Bratanow, T.; Ecer, A.; Kobiske, M.

1974-01-01

An analytical procedure based on the Navier-Stokes equations was developed for analyzing and representing properties of unsteady viscous flow around oscillating obstacles. A variational formulation of the vorticity transport equation was discretized in finite element form and integrated numerically. At each time step of the numerical integration, the velocity field around the obstacle was determined for the instantaneous vorticity distribution from the finite element solution of Poisson's equation. The time-dependent boundary conditions around the oscillating obstacle were introduced as external constraints, using the Lagrangian Multiplier Technique, at each time step of the numerical integration. The procedure was then applied for determining pressures around obstacles oscillating in unsteady flow. The obtained results for a cylinder and an airfoil were illustrated in the form of streamlines and vorticity and pressure distributions.

Steady state model for the thermal regimes of shells of airships and hot air balloons

NASA Astrophysics Data System (ADS)

Luchev, Oleg A.

1992-10-01

A steady state model of the temperature regime of airships and hot air balloons shells is developed. The model includes three governing equations: the equation of the temperature field of airships or balloons shell, the integral equation for the radiative fluxes on the internal surface of the shell, and the integral equation for the natural convective heat exchange between the shell and the internal gas. In the model the following radiative fluxes on the shell external surface are considered: the direct and the earth reflected solar radiation, the diffuse solar radiation, the infrared radiation of the earth surface and that of the atmosphere. For the calculations of the infrared external radiation the model of the plane layer of the atmosphere is used. The convective heat transfer on the external surface of the shell is considered for the cases of the forced and the natural convection. To solve the mentioned set of the equations the numerical iterative procedure is developed. The model and the numerical procedure are used for the simulation study of the temperature fields of an airship shell under the forced and the natural convective heat transfer.

Error Propagation Dynamics of PIV-based Pressure Field Calculations: How well does the pressure Poisson solver perform inherently?

PubMed

Pan, Zhao; Whitehead, Jared; Thomson, Scott; Truscott, Tadd

2016-08-01

Obtaining pressure field data from particle image velocimetry (PIV) is an attractive technique in fluid dynamics due to its noninvasive nature. The application of this technique generally involves integrating the pressure gradient or solving the pressure Poisson equation using a velocity field measured with PIV. However, very little research has been done to investigate the dynamics of error propagation from PIV-based velocity measurements to the pressure field calculation. Rather than measure the error through experiment, we investigate the dynamics of the error propagation by examining the Poisson equation directly. We analytically quantify the error bound in the pressure field, and are able to illustrate the mathematical roots of why and how the Poisson equation based pressure calculation propagates error from the PIV data. The results show that the error depends on the shape and type of boundary conditions, the dimensions of the flow domain, and the flow type.

Numerical solutions of Navier-Stokes equations for a Butler wing

NASA Technical Reports Server (NTRS)

Abolhassani, J. S.; Tiwari, S. N.

1985-01-01

The flow field is simulated on the surface of a given delta wing (Butler wing) at zero incident in a uniform stream. The simulation is done by integrating a set of flow field equations. This set of equations governs the unsteady, viscous, compressible, heat conducting flow of an ideal gas. The equations are written in curvilinear coordinates so that the wing surface is represented accurately. These equations are solved by the finite difference method, and results obtained for high-speed freestream conditions are compared with theoretical and experimental results. In this study, the Navier-Stokes equations are solved numerically. These equations are unsteady, compressible, viscous, and three-dimensional without neglecting any terms. The time dependency of the governing equations allows the solution to progress naturally for an arbitrary initial initial guess to an asymptotic steady state, if one exists. The equations are transformed from physical coordinates to the computational coordinates, allowing the solution of the governing equations in a rectangular parallel-piped domain. The equations are solved by the MacCormack time-split technique which is vectorized and programmed to run on the CDC VPS 32 computer.

The Application of a Boundary Integral Equation Method to the Prediction of Ducted Fan Engine Noise

NASA Technical Reports Server (NTRS)

Dunn, M. H.; Tweed, J.; Farassat, F.

1999-01-01

The prediction of ducted fan engine noise using a boundary integral equation method (BIEM) is considered. Governing equations for the BIEM are based on linearized acoustics and describe the scattering of incident sound by a thin, finite-length cylindrical duct in the presence of a uniform axial inflow. A classical boundary value problem (BVP) is derived that includes an axisymmetric, locally reacting liner on the duct interior. Using potential theory, the BVP is recast as a system of hypersingular boundary integral equations with subsidiary conditions. We describe the integral equation derivation and solution procedure in detail. The development of the computationally efficient ducted fan noise prediction program TBIEM3D, which implements the BIEM, and its utility in conducting parametric noise reduction studies are discussed. Unlike prediction methods based on spinning mode eigenfunction expansions, the BIEM does not require the decomposition of the interior acoustic field into its radial and axial components which, for the liner case, avoids the solution of a difficult complex eigenvalue problem. Numerical spectral studies are presented to illustrate the nexus between the eigenfunction expansion representation and BIEM results. We demonstrate BIEM liner capability by examining radiation patterns for several cases of practical interest.

Parallel heat transport in integrable and chaotic magnetic fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Del-Castillo-Negrete, Diego B; Chacon, Luis

2012-01-01

The study of transport in magnetized plasmas is a problem of fundamental interest in controlled fusion, space plasmas, and astrophysics research. Three issues make this problem particularly chal- lenging: (i) The extreme anisotropy between the parallel (i.e., along the magnetic field), , and the perpendicular, , conductivities ( / may exceed 1010 in fusion plasmas); (ii) Magnetic field lines chaos which in general complicates (and may preclude) the construction of magnetic field line coordinates; and (iii) Nonlocal parallel transport in the limit of small collisionality. Motivated by these issues, we present a Lagrangian Green s function method to solve themore » local and non-local parallel transport equation applicable to integrable and chaotic magnetic fields in arbitrary geom- etry. The method avoids by construction the numerical pollution issues of grid-based algorithms. The potential of the approach is demonstrated with nontrivial applications to integrable (magnetic island chain), weakly chaotic (devil s staircase), and fully chaotic magnetic field configurations. For the latter, numerical solutions of the parallel heat transport equation show that the effective radial transport, with local and non-local closures, is non-diffusive, thus casting doubts on the appropriateness of the applicability of quasilinear diffusion descriptions. General conditions for the existence of non-diffusive, multivalued flux-gradient relations in the temperature evolution are derived.« less

Mathematical modelling of the destruction degree of cancer under the influence of a RF hyperthermia

NASA Astrophysics Data System (ADS)

Paruch, Marek; Turchan, Łukasz

2018-01-01

The article presents the mathematical modeling of the phenomenon of artificial hyperthermia which is caused by the interaction of an electric field. The electric field is induced by the applicator positioned within the biological tissue with cancer. In addition, in order to estimate the degree of tumor destruction under the influence of high temperature an Arrhenius integral has been used. The distribution of electric potential in the domain considered is described by the Laplace system of equations, while the temperature field is described by the Pennes system of equations. These problems are coupled by source function being the additional component in the Pennes equation and resulting from the electric field action. The boundary element method is applied to solve the coupled problem connected with the heating of biological tissues.

Combined effects of magnetic field and partial slip on obliquely striking rheological fluid over a stretching surface

NASA Astrophysics Data System (ADS)

Nadeem, S.; Mehmood, Rashid; Akbar, Noreen Sher

2015-03-01

This study explores the collective effects of partial slip and transverse magnetic field on an oblique stagnation point flow of a rheological fluid. The prevailing momentum equations are designed by manipulating Casson fluid model. By applying the suitable similarity transformations, the governing system of equations is being transformed into coupled nonlinear ordinary differential equations. The resulting system is handled numerically through midpoint integration scheme together with Richardson's extrapolation. It is found that both normal and tangential velocity profiles decreases with an increase in magnetic field as well as slip parameter. Streamlines pattern are presented to study the actual impact of slip mechanism and magnetic field on the oblique flow. A suitable comparison with the previous literature is also provided to confirm the accuracy of present results for the limiting case.

Master equations and the theory of stochastic path integrals

NASA Astrophysics Data System (ADS)

Weber, Markus F.; Frey, Erwin

2017-04-01

This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of master equations most often rely on low-noise approximations such as the Kramers-Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations. We focus on numerical and analytical methods going beyond the low-noise limit and provide a unified framework for the study of master equations. After deriving the forward and backward master equations from the Chapman-Kolmogorov equation, we show how the two master equations can be cast into either of four linear partial differential equations (PDEs). Three of these PDEs are discussed in detail. The first PDE governs the time evolution of a generalized probability generating function whose basis depends on the stochastic process under consideration. Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE. The second PDE is novel and is obeyed by a distribution that is marginalized over an initial state. It proves useful for the computation of mean extinction times. The third PDE describes the time evolution of a ‘generating functional’, which generalizes the so-called Poisson representation. Subsequently, the solutions of the PDEs are expressed in terms of two path integrals: a ‘forward’ and a ‘backward’ path integral. Combined with inverse transformations, one obtains two distinct path integral representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Moreover, we show how a well-known path integral representation of averaged observables can be recovered from them. Upon expanding the forward and the backward path integrals around stationary paths, we then discuss and extend a recent method for the computation of rare event probabilities. Besides, we also derive path integral representations for processes with continuous state spaces whose forward and backward master equations admit Kramers-Moyal expansions. A truncation of the backward expansion at the level of a diffusion approximation recovers a classic path integral representation of the (backward) Fokker-Planck equation. One can rewrite this path integral in terms of an Onsager-Machlup function and, for purely diffusive Brownian motion, it simplifies to the path integral of Wiener. To make this review accessible to a broad community, we have used the language of probability theory rather than quantum (field) theory and do not assume any knowledge of the latter. The probabilistic structures underpinning various technical concepts, such as coherent states, the Doi-shift, and normal-ordered observables, are thereby made explicit.

Master equations and the theory of stochastic path integrals.

PubMed

Weber, Markus F; Frey, Erwin

2017-04-01

This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of master equations most often rely on low-noise approximations such as the Kramers-Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations. We focus on numerical and analytical methods going beyond the low-noise limit and provide a unified framework for the study of master equations. After deriving the forward and backward master equations from the Chapman-Kolmogorov equation, we show how the two master equations can be cast into either of four linear partial differential equations (PDEs). Three of these PDEs are discussed in detail. The first PDE governs the time evolution of a generalized probability generating function whose basis depends on the stochastic process under consideration. Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE. The second PDE is novel and is obeyed by a distribution that is marginalized over an initial state. It proves useful for the computation of mean extinction times. The third PDE describes the time evolution of a 'generating functional', which generalizes the so-called Poisson representation. Subsequently, the solutions of the PDEs are expressed in terms of two path integrals: a 'forward' and a 'backward' path integral. Combined with inverse transformations, one obtains two distinct path integral representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Moreover, we show how a well-known path integral representation of averaged observables can be recovered from them. Upon expanding the forward and the backward path integrals around stationary paths, we then discuss and extend a recent method for the computation of rare event probabilities. Besides, we also derive path integral representations for processes with continuous state spaces whose forward and backward master equations admit Kramers-Moyal expansions. A truncation of the backward expansion at the level of a diffusion approximation recovers a classic path integral representation of the (backward) Fokker-Planck equation. One can rewrite this path integral in terms of an Onsager-Machlup function and, for purely diffusive Brownian motion, it simplifies to the path integral of Wiener. To make this review accessible to a broad community, we have used the language of probability theory rather than quantum (field) theory and do not assume any knowledge of the latter. The probabilistic structures underpinning various technical concepts, such as coherent states, the Doi-shift, and normal-ordered observables, are thereby made explicit.

Hybrid finite element method for describing the electrical response of biological cells to applied fields.

PubMed

Ying, Wenjun; Henriquez, Craig S

2007-04-01

A novel hybrid finite element method (FEM) for modeling the response of passive and active biological membranes to external stimuli is presented. The method is based on the differential equations that describe the conservation of electric flux and membrane currents. By introducing the electric flux through the cell membrane as an additional variable, the algorithm decouples the linear partial differential equation part from the nonlinear ordinary differential equation part that defines the membrane dynamics of interest. This conveniently results in two subproblems: a linear interface problem and a nonlinear initial value problem. The linear interface problem is solved with a hybrid FEM. The initial value problem is integrated by a standard ordinary differential equation solver such as the Euler and Runge-Kutta methods. During time integration, these two subproblems are solved alternatively. The algorithm can be used to model the interaction of stimuli with multiple cells of almost arbitrary geometries and complex ion-channel gating at the plasma membrane. Numerical experiments are presented demonstrating the uses of the method for modeling field stimulation and action potential propagation.

An efficient model for coupling structural vibrations with acoustic radiation

NASA Technical Reports Server (NTRS)

Frendi, Abdelkader; Maestrello, Lucio; Ting, LU

1993-01-01

The scattering of an incident wave by a flexible panel is studied. The panel vibration is governed by the nonlinear plate equations while the loading on the panel, which is the pressure difference across the panel, depends on the reflected and transmitted waves. Two models are used to calculate this structural-acoustic interaction problem. One solves the three dimensional nonlinear Euler equations for the flow-field coupled with the plate equations (the fully coupled model). The second uses the linear wave equation for the acoustic field and expresses the load as a double integral involving the panel oscillation (the decoupled model). The panel oscillation governed by a system of integro-differential equations is solved numerically and the acoustic field is then defined by an explicit formula. Numerical results are obtained using the two models for linear and nonlinear panel vibrations. The predictions given by these two models are in good agreement but the computational time needed for the 'fully coupled model' is 60 times longer than that for 'the decoupled model'.

Large eddy simulation of incompressible turbulent channel flow

NASA Technical Reports Server (NTRS)

Moin, P.; Reynolds, W. C.; Ferziger, J. H.

1978-01-01

The three-dimensional, time-dependent primitive equations of motion were numerically integrated for the case of turbulent channel flow. A partially implicit numerical method was developed. An important feature of this scheme is that the equation of continuity is solved directly. The residual field motions were simulated through an eddy viscosity model, while the large-scale field was obtained directly from the solution of the governing equations. An important portion of the initial velocity field was obtained from the solution of the linearized Navier-Stokes equations. The pseudospectral method was used for numerical differentiation in the horizontal directions, and second-order finite-difference schemes were used in the direction normal to the walls. The large eddy simulation technique is capable of reproducing some of the important features of wall-bounded turbulent flows. The resolvable portions of the root-mean square wall pressure fluctuations, pressure velocity-gradient correlations, and velocity pressure-gradient correlations are documented.

Multiparticle dynamics in an expanding universe

NASA Astrophysics Data System (ADS)

Anderson, James L.

1995-11-01

Approximate equations of motion for multiparticle systems in an expanding Einstein-deSitter universe are derived from the Einstein-Maxwell field equations using the Einstein-Infeld-Hoffmann surface integral method. At the Newtonian level of approximation one finds that, in comoving coordinates, both the Newtonian gravitational and Coulomb interactions in these equations are multiplied by the inverse third power of the scale factor R(t) appearing in the Einstein-deSitter field and they acquire a cosmic ``drag'' term. Nevertheless, both the period and luminosity size of bound two-body systems whose period is small compared to the Hubble time are found to be independent of t.

Noether symmetries and stability of ideal gas solutions in Galileon cosmology

NASA Astrophysics Data System (ADS)

Dimakis, N.; Giacomini, Alex; Jamal, Sameerah; Leon, Genly; Paliathanasis, Andronikos

2017-03-01

A class of generalized Galileon cosmological models, which can be described by a pointlike Lagrangian, is considered in order to utilize Noether's theorem to determine conservation laws for the field equations. In the Friedmann-Lemaître-Robertson-Walker universe, the existence of a nontrivial conservation law indicates the integrability of the field equations. Because of the complexity of the latter, we apply the differential invariants approach in order to construct special power-law solutions and study their stability.

Estimation of Planetary Wave Parameters from the Data of the 1981 Ocean Acoustic Tomography Experiment.

DTIC Science & Technology

1985-10-01

can monitor a larger region and provide a larger database with fewer moorings, and its averaging (integrating) process can filter out undesirable small...as the eikonal equation, relating o to the perturbed sound-speed field Z+6c and the flow field v during ,*.. a transmission by .= (c*-v VO) 2 /(F+6c...should consult Spiesberger et al. (1980) for ray identifications. Ugincius (1970) solved the eikonal equation using the method of -. characteristics

Electromagnetic Field Penetration Studies

NASA Technical Reports Server (NTRS)

Deshpande, M.D.

2000-01-01

A numerical method is presented to determine electromagnetic shielding effectiveness of rectangular enclosure with apertures on its wall used for input and output connections, control panels, visual-access windows, ventilation panels, etc. Expressing EM fields in terms of cavity Green's function inside the enclosure and the free space Green's function outside the enclosure, integral equations with aperture tangential electric fields as unknown variables are obtained by enforcing the continuity of tangential electric and magnetic fields across the apertures. Using the Method of Moments, the integral equations are solved for unknown aperture fields. From these aperture fields, the EM field inside a rectangular enclosure due to external electromagnetic sources are determined. Numerical results on electric field shielding of a rectangular cavity with a thin rectangular slot obtained using the present method are compared with the results obtained using simple transmission line technique for code validation. The present technique is applied to determine field penetration inside a Boeing-757 by approximating its passenger cabin as a rectangular cavity filled with a homogeneous medium and its passenger windows by rectangular apertures. Preliminary results for, two windows, one on each side of fuselage were considered. Numerical results for Boeing-757 at frequencies 26 MHz, 171-175 MHz, and 428-432 MHz are presented.

Improved algorithms and methods for room sound-field prediction by acoustical radiosity in arbitrary polyhedral rooms.

PubMed

Nosal, Eva-Marie; Hodgson, Murray; Ashdown, Ian

2004-08-01

This paper explores acoustical (or time-dependent) radiosity--a geometrical-acoustics sound-field prediction method that assumes diffuse surface reflection. The literature of acoustical radiosity is briefly reviewed and the advantages and disadvantages of the method are discussed. A discrete form of the integral equation that results from meshing the enclosure boundaries into patches is presented and used in a discrete-time algorithm. Furthermore, an averaging technique is used to reduce computational requirements. To generalize to nonrectangular rooms, a spherical-triangle method is proposed as a means of evaluating the integrals over solid angles that appear in the discrete form of the integral equation. The evaluation of form factors, which also appear in the numerical solution, is discussed for rectangular and nonrectangular rooms. This algorithm and associated methods are validated by comparison of the steady-state predictions for a spherical enclosure to analytical solutions.

Improved algorithms and methods for room sound-field prediction by acoustical radiosity in arbitrary polyhedral rooms

NASA Astrophysics Data System (ADS)

Nosal, Eva-Marie; Hodgson, Murray; Ashdown, Ian

2004-08-01

This paper explores acoustical (or time-dependent) radiosity-a geometrical-acoustics sound-field prediction method that assumes diffuse surface reflection. The literature of acoustical radiosity is briefly reviewed and the advantages and disadvantages of the method are discussed. A discrete form of the integral equation that results from meshing the enclosure boundaries into patches is presented and used in a discrete-time algorithm. Furthermore, an averaging technique is used to reduce computational requirements. To generalize to nonrectangular rooms, a spherical-triangle method is proposed as a means of evaluating the integrals over solid angles that appear in the discrete form of the integral equation. The evaluation of form factors, which also appear in the numerical solution, is discussed for rectangular and nonrectangular rooms. This algorithm and associated methods are validated by comparison of the steady-state predictions for a spherical enclosure to analytical solutions.

The complete Brans–Dicke theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kofinas, Georgios, E-mail: gkofinas@aegean.gr

Given that the simple wave equation of Brans–Dicke theory for the scalar field is preserved, we have investigated, through exhaustively analyzing the Bianchi identities, the consistent theories which violate the exact energy conservation equation. It is found that only three theories exist which are unambiguously determined from consistency, without imposing arbitrary functions by hand. Each of these theories possesses a specific interaction term which controls the energy exchange between the scalar field and ordinary matter. The theories contain new parameters (integration constants from the integration procedure) and when these are switched-off, Brans–Dicke theory emerges. As usually, the vacuum theories canmore » be defined from the complete Brans–Dicke theories when the matter energy–momentum tensor vanishes.« less

Analysis of scattering by a linear chain of spherical inclusions in an optical fiber

NASA Astrophysics Data System (ADS)

Chremmos, Ioannis D.; Uzunoglu, Nikolaos K.

2006-12-01

The scattering by a linear chain of spherical dielectric inclusions, embedded along the axis of an optical fiber, is analyzed using a rigorous integral equation formulation, based on the dyadic Green's function theory. The coupled electric field integral equations are solved by applying the Galerkin technique with Mie-type expansion of the field inside the spheres in terms of spherical waves. The analysis extends the previously studied case of a single spherical inhomogeneity inside a fiber to the multisphere-scattering case, by utilizing the classic translational addition theorems for spherical waves in order to analytically extract the direct-intersphere-coupling coefficients. Results for the transmitted and reflected power, on incidence of the fundamental HE11 mode, are presented for several cases.

Landau ghost pole problem in quantum field theory: From 50th of last century to the present day

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jafarov, Rauf G., E-mail: rauf-jafarov@hotmail.com; Mutallimov, Mutallim M.

2016-03-25

In this paper we present our results of the investigation of asymptotical behavior of amplitude at short distances in four-dimensional scalar field theory with ϕ{sup 4} interaction. To formulate of our calculating model – two-particle approximation of the mean-field expansion we have used an Rochev’s iteration scheme of solution of the Schwinger-Dyson equations with the fermion bilocal source. We have considered the nonlinear integral equations in deep-inelastic region of momenta. As result we have a non-trivial behavior of amplitude at large momenta.

Self-dual monopoles and toda molecules

NASA Astrophysics Data System (ADS)

Ganoulis, N.; Goddard, P.; Olive, D.

1982-07-01

Stable static solutions to a gauge field theory with a Higgs field in the adjoint representation and with vanishing self-coupling are self-dual in the sense of Bogomolny. Leznov and Saveliev showed that a specific form of spherical symmetry reduces these equations to a modified form of the Toda molecule equations associated with the overall gauge symmetry G. Values of the constants of integration are found in terms of the distant Higgs field, guaranteeing regularity of the solution at the origin. The expressions hold for any simple Lie group G, depending on G via its root system.

Differential renormalization-group generators for static and dynamic critical phenomena

NASA Astrophysics Data System (ADS)

Chang, T. S.; Vvedensky, D. D.; Nicoll, J. F.

1992-09-01

The derivation of differential renormalization-group (DRG) equations for applications to static and dynamic critical phenomena is reviewed. The DRG approach provides a self-contained closed-form representation of the Wilson renormalization group (RG) and should be viewed as complementary to the Callan-Symanzik equations used in field-theoretic approaches to the RG. The various forms of DRG equations are derived to illustrate the general mathematical structure of each approach and to point out the advantages and disadvantages for performing practical calculations. Otherwise, the review focuses upon the one-particle-irreducible DRG equations derived by Nicoll and Chang and by Chang, Nicoll, and Young; no attempt is made to provide a general treatise of critical phenomena. A few specific examples are included to illustrate the utility of the DRG approach: the large- n limit of the classical n-vector model (the spherical model), multi- or higher-order critical phenomena, and crit ical dynamics far from equilibrium. The large- n limit of the n-vector model is used to introduce the application of DRG equations to a well-known example, with exact solution obtained for the nonlinear trajectories, generating functions for nonlinear scaling fields, and the equation of state. Trajectory integrals and nonlinear scaling fields within the framework of ɛ-expansions are then discussed for tricritical crossover, and briefly for certain aspects of multi- or higher-order critical points, including the derivation of the Helmholtz free energy and the equation of state. The discussion then turns to critical dynamics with a development of the path integral formulation for general dynamic processes. This is followed by an application to a model far-from-equilibrium system that undergoes a phase transformation analogous to a second-order critical point, the Schlögl model for a chemical instability.

Multiscale solvers and systematic upscaling in computational physics

NASA Astrophysics Data System (ADS)

Brandt, A.

2005-07-01

Multiscale algorithms can overcome the scale-born bottlenecks that plague most computations in physics. These algorithms employ separate processing at each scale of the physical space, combined with interscale iterative interactions, in ways which use finer scales very sparingly. Having been developed first and well known as multigrid solvers for partial differential equations, highly efficient multiscale techniques have more recently been developed for many other types of computational tasks, including: inverse PDE problems; highly indefinite (e.g., standing wave) equations; Dirac equations in disordered gauge fields; fast computation and updating of large determinants (as needed in QCD); fast integral transforms; integral equations; astrophysics; molecular dynamics of macromolecules and fluids; many-atom electronic structures; global and discrete-state optimization; practical graph problems; image segmentation and recognition; tomography (medical imaging); fast Monte-Carlo sampling in statistical physics; and general, systematic methods of upscaling (accurate numerical derivation of large-scale equations from microscopic laws).

A fast and well-conditioned spectral method for singular integral equations

NASA Astrophysics Data System (ADS)

Slevinsky, Richard Mikael; Olver, Sheehan

2017-03-01

We develop a spectral method for solving univariate singular integral equations over unions of intervals by utilizing Chebyshev and ultraspherical polynomials to reformulate the equations as almost-banded infinite-dimensional systems. This is accomplished by utilizing low rank approximations for sparse representations of the bivariate kernels. The resulting system can be solved in O (m2 n) operations using an adaptive QR factorization, where m is the bandwidth and n is the optimal number of unknowns needed to resolve the true solution. The complexity is reduced to O (mn) operations by pre-caching the QR factorization when the same operator is used for multiple right-hand sides. Stability is proved by showing that the resulting linear operator can be diagonally preconditioned to be a compact perturbation of the identity. Applications considered include the Faraday cage, and acoustic scattering for the Helmholtz and gravity Helmholtz equations, including spectrally accurate numerical evaluation of the far- and near-field solution. The JULIA software package SingularIntegralEquations.jl implements our method with a convenient, user-friendly interface.

Lattice properties of the Phase I BNL x-ray lithography source obtained from fits to magnetic measurement data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Blumberg, L.N.; Murphy, J.B.; Reusch, M.F.

1991-01-01

The orbit, tune, chromaticity and {beta} values for the Phase 1 XLS ring were computed by numerical integration of equations of motion using fields obtained from the coefficients of the 3-dimensional solution of Laplace's Equation evaluated by fits to magnetic measurements. The results are in good agreement with available data. The method has been extended to higher order fits of TOSCA generated fields in planes normal to the reference axis using the coil configuration proposed for the Superconducting X-Ray Lithography Source. Agreement with results from numerical integration through fields given directly by TOSCA is excellent. The formulation of the normalmore » multipole expansion presented by Brown and Servranckx has been extended to include skew multipole terms. The method appears appropriate for analysis of magnetic measurements of the SXLS. 8 refs. , 2 figs., 2 tabs.« less

Rapid analysis of scattering from periodic dielectric structures using accelerated Cartesian expansions.

PubMed

Baczewski, Andrew D; Miller, Nicholas C; Shanker, Balasubramaniam

2012-04-01

The analysis of fields in periodic dielectric structures arise in numerous applications of recent interest, ranging from photonic bandgap structures and plasmonically active nanostructures to metamaterials. To achieve an accurate representation of the fields in these structures using numerical methods, dense spatial discretization is required. This, in turn, affects the cost of analysis, particularly for integral-equation-based methods, for which traditional iterative methods require O(N2) operations, N being the number of spatial degrees of freedom. In this paper, we introduce a method for the rapid solution of volumetric electric field integral equations used in the analysis of doubly periodic dielectric structures. The crux of our method is the accelerated Cartesian expansion algorithm, which is used to evaluate the requisite potentials in O(N) cost. Results are provided that corroborate our claims of acceleration without compromising accuracy, as well as the application of our method to a number of compelling photonics applications.

PREFACE: Symmetries and Integrability of Difference Equations

NASA Astrophysics Data System (ADS)

Doliwa, Adam; Korhonen, Risto; Lafortune, Stéphane

2007-10-01

The notion of integrability was first introduced in the 19th century in the context of classical mechanics with the definition of Liouville integrability for Hamiltonian flows. Since then, several notions of integrability have been introduced for partial and ordinary differential equations. Closely related to integrability theory is the symmetry analysis of nonlinear evolution equations. Symmetry analysis takes advantage of the Lie group structure of a given equation to study its properties. Together, integrability theory and symmetry analysis provide the main method by which nonlinear evolution equations can be solved explicitly. Difference equations (DE), like differential equations, are important in numerous fields of science and have a wide variety of applications in such areas as mathematical physics, computer visualization, numerical analysis, mathematical biology, economics, combinatorics, and quantum field theory. It is thus crucial to develop tools to study and solve DEs. While the theory of symmetry and integrability for differential equations is now largely well-established, this is not yet the case for discrete equations. Although over recent years there has been significant progress in the development of a complete analytic theory of difference equations, further tools are still needed to fully understand, for instance, the symmetries, asymptotics and the singularity structure of difference equations. The series of SIDE meetings on Symmetries and Integrability of Difference Equations started in 1994. Its goal is to provide a platform for an international and interdisciplinary communication for researchers working in areas associated with integrable discrete systems, such as classical and quantum physics, computer science and numerical analysis, mathematical biology and economics, discrete geometry and combinatorics, theory of special functions, etc. The previous SIDE meetings took place in Estérel near Montréal, Canada (1994), at the University of Kent in Canterbury, UK (1996), in Sabaudia near Rome, Italy (1998), at the University of Tokyo, Japan (2000), in Giens, France (2002), and in Helsinki, Finland (2004). The SIDE VII meeting was held at the University of Melbourne from 10-14 July 2006. The scientific committee consisted of Nalini Joshi (The University of Sydney), Frank W Nijhoff (University of Leeds), Reinout Quispel (La Trobe University) and Colin Rogers (University of New South Wales). The local organization was in the hands of John A G Roberts and Wolfgang K Schief. Proceedings of all the previous SIDE meetings have been published; the 1994 and 1988 meetings (edited respectively by D Levi, L Vinet and P Winternitz, and by D Levi and O Ragnisco) as volumes of the CRM Proceedings and Lecture Notes (AMS Publications), the 1996 meeting (edited by P Clarkson and F W Nijhoff) as Volume 255 in the LMS Lecture Note Series. Starting from the 1996 meeting the formula of publication has been changed to include rather selected refereed contributions submitted in response to a call for papers issued after the meetings and not restricted to their participants. Thus publications reflecting the scope of the 1996 meeting (edited by J Hietarinta, F W Nijhoff and J Satsuma) appeared in Journal of Physics A: Mathematical and General 34 48 (special issue), and of the 1998 and 2000 meetings (edited respectively by F W Nijhoff, Yu B Suris and C-M Viallet, and by J F van Diejen and R Halburd) in Journal of Nonlinear Mathematical Physics 10 (Suppl. 2) and 12 (Suppl. 2). The aim of this special issue is to benefit from the occasion offered by the SIDE VII meeting, producing an issue containing papers which represent the state-of-the-art knowledge for studying integrability and symmetry properties of difference equations. This special issue features high quality research papers and invited reviews which deal with themes that were covered by the SIDE VII conference. These are in alphabetical order: Algebraic-geometric approaches to integrability. The first section contains a paper by T Hamamoto and K Kajiwara on hypergeometric solutions to the q-Painlevé equation of type A4(1). Discrete geometry. In this category there are three papers. J Cielinski offers a geometric definition and a spectral approach on pseudospherical surfaces on time scales, while A Doliwa considers generalized isothermic lattices. The paper by U Pinkall, B Springborn and S Weiss mann is concerned with a new doubly discrete analogue of smoke ring flow and the real time simulation of fluid flow. Integrable systems in statistical physics. Under this heading there is a paper by R J Baxter on corner transfer matrices in statistical mechanics, and a paper by S Boukraa, S Hassani, J-M Maillard, B M McCoy, J-A Weil and N Zenine where the authors consider Fuchs-Painlevé elliptic representation of the Painlevé VI equation. KP lattices and differential-difference hierarchies. In this section we have seven articles. C R Gilson, J J C Nimmo and Y Ohta consider quasideterminant solutions of a non-Abelian Hirota-Miwa equation, while B Grammaticos, A Ramani, V Papageorgiou, J Satsuma and R Willox discuss the construction of lump-like solutions of the Hirota-Miwa equation. J Hietarinta and C Viallet analyze the factorization process for lattice maps searching for integrable cases, the paper by X-B Hu and G-F Yu is concerned with integrable discretizations of the (2+1)-dimensional sinh-Gordon equation, and K Kajiwara, M Mazzocco and Y Ohta consider the Hankel determinant formula of the tau-functions of the Toda equation. Finally, V G Papageorgiou and A G Tongas study Yang-Baxter maps and multi-field integrable lattice equations, and H-Y Wang, X-B Hu and H-W Tam consider the two-dimensional Leznov lattice equation with self-consistent sources. Quantum integrable systems. This category contains a paper on q-extended eigenvectors of the integral and finite Fourier transforms by N M Atakishiyev, J P Rueda and K B Wolf, and an article by S M Sergeev on quantization of three-wave equations. Random matrix theory. This section contains a paper by A V Kitaev on the boundary conditions for scaled random matrix ensembles in the bulk of the spectrum. Symmetries and conservation laws. In this section we have five articles. H Gegen, X-B Hu, D Levi and S Tsujimoto consider a difference-analogue of Davey-Stewartson system giving its discrete Gram-type determinant solution and Lax pair. The paper by D Levi, M Petrera, and C Scimiterna is about the lattice Schwarzian KDV equation and its symmetries, while O G Rasin and P E Hydon study the conservation laws for integrable difference equations. S Saito and N Saitoh discuss recurrence equations associated with invariant varieties of periodic points, and P H van der Kamp presents closed-form expressions for integrals of MKDV and sine-Gordon maps. Ultra-discrete systems. This final category contains an article by C Ormerod on connection matrices for ultradiscrete linear problems. We would like to express our sincerest thanks to all contributors, and to everyone involved in compiling this special issue.

Black Holes, Hidden Symmetry and Complete Integrability: Brief Review

NASA Astrophysics Data System (ADS)

Frolov, Valeri P.

This chapter contains a brief review of the remarkable properties of higher dimensional rotating black holes with the spherical topology of the horizon. We demonstrate that these properties are connected with and generated by a special geometrical object, the Principal Conformal Killing-Yano tensor (PCKYT). The most general solution, describing such black holes, Kerr-NUT-ADS metric, admits this structure. Moreover a solution of the Einstein Equations with (or without) a cosmological constant which possesses PCKYT is the Kerr-NUT-ADS metric. This object (PCKYT) is responsible for such remarkable properties of higher dimensional rotating black holes as: (i) complete integrability of geodesic equations and (ii) complete separation of variables of the important field equations.

Acidity in DMSO from the embedded cluster integral equation quantum solvation model.

PubMed

Heil, Jochen; Tomazic, Daniel; Egbers, Simon; Kast, Stefan M

2014-04-01

The embedded cluster reference interaction site model (EC-RISM) is applied to the prediction of acidity constants of organic molecules in dimethyl sulfoxide (DMSO) solution. EC-RISM is based on a self-consistent treatment of the solute's electronic structure and the solvent's structure by coupling quantum-chemical calculations with three-dimensional (3D) RISM integral equation theory. We compare available DMSO force fields with reference calculations obtained using the polarizable continuum model (PCM). The results are evaluated statistically using two different approaches to eliminating the proton contribution: a linear regression model and an analysis of pK(a) shifts for compound pairs. Suitable levels of theory for the integral equation methodology are benchmarked. The results are further analyzed and illustrated by visualizing solvent site distribution functions and comparing them with an aqueous environment.

Exact solutions for coupled Einstein, Dirac, Maxwell, and zero-mass scalar fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Patra, A.C.; Ray, D.

1987-12-01

Coupled equations for Einstein, Maxwell, Dirac, and zero-mass scalar fields studied by Krori, Bhattacharya, and Nandi are integrated for plane-symmetric time-independent case. It is shown that solutions do not exist for the plane-symmetric time-dependent case.

A global multilevel atmospheric model using a vector semi-Lagrangian finite-difference scheme. I - Adiabatic formulation

NASA Technical Reports Server (NTRS)

Bates, J. R.; Moorthi, S.; Higgins, R. W.

1993-01-01

An adiabatic global multilevel primitive equation model using a two time-level, semi-Lagrangian semi-implicit finite-difference integration scheme is presented. A Lorenz grid is used for vertical discretization and a C grid for the horizontal discretization. The momentum equation is discretized in vector form, thus avoiding problems near the poles. The 3D model equations are reduced by a linear transformation to a set of 2D elliptic equations, whose solution is found by means of an efficient direct solver. The model (with minimal physics) is integrated for 10 days starting from an initialized state derived from real data. A resolution of 16 levels in the vertical is used, with various horizontal resolutions. The model is found to be stable and efficient, and to give realistic output fields. Integrations with time steps of 10 min, 30 min, and 1 h are compared, and the differences are found to be acceptable.

The Scattering of Partially Coherent Electromagnetic Beam Illumination from Statistically Rough Surfaces

DTIC Science & Technology

2014-06-19

scattering research performed by the radio - frequency /microwave and visible/near-infrared communities for synthetic aperture radar and remote...Rough Surfaces with Arbitrary Slope and Frequency ,” IEEE Trans. Antennas Propag. 28, 11 - 21 (1980). 76. E. Bahar, “Full-Wave Solutions for the...equations ..................................................................................... 11 2.2.1 Electric-field integral equations

Fokker-Planck equation of the reduced Wigner function associated to an Ohmic quantum Langevin dynamics

NASA Astrophysics Data System (ADS)

Colmenares, Pedro J.

2018-05-01

This article has to do with the derivation and solution of the Fokker-Planck equation associated to the momentum-integrated Wigner function of a particle subjected to a harmonic external field in contact with an ohmic thermal bath of quantum harmonic oscillators. The strategy employed is a simplified version of the phenomenological approach of Schramm, Jung, and Grabert of interpreting the operators as c numbers to derive the quantum master equation arising from a twofold transformation of the Wigner function of the entire phase space. The statistical properties of the random noise comes from the integral functional theory of Grabert, Schramm, and Ingold. By means of a single Wigner transformation, a simpler equation than that mentioned before is found. The Wigner function reproduces the known results of the classical limit. This allowed us to rewrite the underdamped classical Langevin equation as a first-order stochastic differential equation with time-dependent drift and diffusion terms.

Integral Equations in Computational Electromagnetics: Formulations, Properties and Isogeometric Analysis

NASA Astrophysics Data System (ADS)

Lovell, Amy Elizabeth

Computational electromagnetics (CEM) provides numerical methods to simulate electromagnetic waves interacting with its environment. Boundary integral equation (BIE) based methods, that solve the Maxwell's equations in the homogeneous or piecewise homogeneous medium, are both efficient and accurate, especially for scattering and radiation problems. Development and analysis electromagnetic BIEs has been a very active topic in CEM research. Indeed, there are still many open problems that need to be addressed or further studied. A short and important list includes (1) closed-form or quasi-analytical solutions to time-domain integral equations, (2) catastrophic cancellations at low frequencies, (3) ill-conditioning due to high mesh density, multi-scale discretization, and growing electrical size, and (4) lack of flexibility due to re-meshing when increasing number of forward numerical simulations are involved in the electromagnetic design process. This dissertation will address those several aspects of boundary integral equations in computational electromagnetics. The first contribution of the dissertation is to construct quasi-analytical solutions to time-dependent boundary integral equations using a direct approach. Direct inverse Fourier transform of the time-harmonic solutions is not stable due to the non-existence of the inverse Fourier transform of spherical Hankel functions. Using new addition theorems for the time-domain Green's function and dyadic Green's functions, time-domain integral equations governing transient scattering problems of spherical objects are solved directly and stably for the first time. Additional, the direct time-dependent solutions, together with the newly proposed time-domain dyadic Green's functions, can enrich the time-domain spherical multipole theory. The second contribution is to create a novel method of moments (MoM) framework to solve electromagnetic boundary integral equation on subdivision surfaces. The aim is to avoid the meshing and re-meshing stages to accelerate the design process when the geometry needs to be updated. Two schemes to construct basis functions on the subdivision surface have been explored. One is to use the div-conforming basis function, and the other one is to create a rigorous iso-geometric approach based on the subdivision basis function with better smoothness properties. This new framework provides us better accuracy, more stability and high flexibility. The third contribution is a new stable integral equation formulation to avoid catastrophic cancellations due to low-frequency breakdown or dense-mesh breakdown. Many of the conventional integral equations and their associated post-processing operations suffer from numerical catastrophic cancellations, which can lead to ill-conditioning of the linear systems or serious accuracy problems. Examples includes low-frequency breakdown and dense mesh breakdown. Another instability may come from nontrivial null spaces of involving integral operators that might be related with spurious resonance or topology breakdown. This dissertation presents several sets of new boundary integral equations and studies their analytical properties. The first proposed formulation leads to the scalar boundary integral equations where only scalar unknowns are involved. Besides the requirements of gaining more stability and better conditioning in the resulting linear systems, multi-physics simulation is another driving force for new formulations. Scalar and vector potentials (rather than electromagnetic field) based formulation have been studied for this purpose. Those new contributions focus on different stages of boundary integral equations in an almost independent manner, e.g. isogeometric analysis framework can be used to solve different boundary integral equations, and the time-dependent solutions to integral equations from different formulations can be achieved through the same methodology proposed.

Finite element-integral simulation of static and flight fan noise radiation from the JT15D turbofan engine

NASA Technical Reports Server (NTRS)

Baumeister, K. J.; Horowitz, S. J.

1982-01-01

An iterative finite element integral technique is used to predict the sound field radiated from the JT15D turbofan inlet. The sound field is divided into two regions: the sound field within and near the inlet which is computed using the finite element method and the radiation field beyond the inlet which is calculated using an integral solution technique. The velocity potential formulation of the acoustic wave equation was employed in the program. For some single mode JT15D data, the theory and experiment are in good agreement for the far field radiation pattern as well as suppressor attenuation. Also, the computer program is used to simulate flight effects that cannot be performed on a ground static test stand.

Toroidal regularization of the guiding center Lagrangian

DOE PAGES

Burby, J. W.; Ellison, C. L.

2017-11-22

In the Lagrangian theory of guiding center motion, an effective magnetic field B* = B+ (m/e)v ∥∇ x b appears prominently in the equations of motion. Because the parallel component of this field can vanish, there is a range of parallel velocities where the Lagrangian guiding center equations of motion are either ill-defined or very badly behaved. Moreover, the velocity dependence of B* greatly complicates the identification of canonical variables and therefore the formulation of symplectic integrators for guiding center dynamics. Here, this letter introduces a simple coordinate transformation that alleviates both these problems simultaneously. In the new coordinates, themore » Liouville volume element is equal to the toroidal contravariant component of the magnetic field. Consequently, the large-velocity singularity is completely eliminated. Moreover, passing from the new coordinate system to canonical coordinates is extremely simple, even if the magnetic field is devoid of flux surfaces. We demonstrate the utility of this approach in regularizing the guiding center Lagrangian by presenting a new and stable one-step variational integrator for guiding centers moving in arbitrary time-dependent electromagnetic fields.« less

Toroidal regularization of the guiding center Lagrangian

DOE Office of Scientific and Technical Information (OSTI.GOV)

Burby, J. W.; Ellison, C. L.

In the Lagrangian theory of guiding center motion, an effective magnetic field B* = B+ (m/e)v ∥∇ x b appears prominently in the equations of motion. Because the parallel component of this field can vanish, there is a range of parallel velocities where the Lagrangian guiding center equations of motion are either ill-defined or very badly behaved. Moreover, the velocity dependence of B* greatly complicates the identification of canonical variables and therefore the formulation of symplectic integrators for guiding center dynamics. Here, this letter introduces a simple coordinate transformation that alleviates both these problems simultaneously. In the new coordinates, themore » Liouville volume element is equal to the toroidal contravariant component of the magnetic field. Consequently, the large-velocity singularity is completely eliminated. Moreover, passing from the new coordinate system to canonical coordinates is extremely simple, even if the magnetic field is devoid of flux surfaces. We demonstrate the utility of this approach in regularizing the guiding center Lagrangian by presenting a new and stable one-step variational integrator for guiding centers moving in arbitrary time-dependent electromagnetic fields.« less

General pulsed-field gradient signal attenuation expression based on a fractional integral modified-Bloch equation

NASA Astrophysics Data System (ADS)

Lin, Guoxing

2018-10-01

Anomalous diffusion has been investigated in many polymer and biological systems. The analysis of PFG anomalous diffusion relies on the ability to obtain the signal attenuation expression. However, the general analytical PFG signal attenuation expression based on the fractional derivative has not been previously reported. Additionally, the reported modified-Bloch equations for PFG anomalous diffusion in the literature yielded different results due to their different forms. Here, a new integral type modified-Bloch equation based on the fractional derivative for PFG anomalous diffusion is proposed, which is significantly different from the conventional differential type modified-Bloch equation. The merit of the integral type modified-Bloch equation is that the original properties of the contributions from linear or nonlinear processes remain unchanged at the instant of the combination. From the modified-Bloch equation, the general solutions are derived, which includes the finite gradient pulse width (FGPW) effect. The numerical evaluation of these PFG signal attenuation expressions can be obtained either by the Adomian decomposition, or a direct integration method that is fast and practicable. The theoretical results agree with the continuous-time random walk (CTRW) simulations performed in this paper. Additionally, the relaxation effect in PFG anomalous diffusion is found to be different from that in PFG normal diffusion. The new modified-Bloch equations and their solutions provide a fundamental tool to analyze PFG anomalous diffusion in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI).

Integral equation methods for vesicle electrohydrodynamics in three dimensions

NASA Astrophysics Data System (ADS)

Veerapaneni, Shravan

2016-12-01

In this paper, we develop a new boundary integral equation formulation that describes the coupled electro- and hydro-dynamics of a vesicle suspended in a viscous fluid and subjected to external flow and electric fields. The dynamics of the vesicle are characterized by a competition between the elastic, electric and viscous forces on its membrane. The classical Taylor-Melcher leaky-dielectric model is employed for the electric response of the vesicle and the Helfrich energy model combined with local inextensibility is employed for its elastic response. The coupled governing equations for the vesicle position and its transmembrane electric potential are solved using a numerical method that is spectrally accurate in space and first-order in time. The method uses a semi-implicit time-stepping scheme to overcome the numerical stiffness associated with the governing equations.

ODE/IM correspondence for modified B2(1) affine Toda field equation

NASA Astrophysics Data System (ADS)

Ito, Katsushi; Shu, Hongfei

2017-03-01

We study the massive ODE/IM correspondence for modified B2(1) affine Toda field equation. Based on the ψ-system for the solutions of the associated linear problem, we obtain the Bethe ansatz equations. We also discuss the T-Q relations, the T-system and the Y-system, which are shown to be related to those of the A3 /Z2 integrable system. We consider the case that the solution of the linear problem has a monodromy around the origin, which imposes nontrivial boundary conditions for the T-/Y-system. The high-temperature limit of the T- and Y-system and their monodromy dependence are studied numerically.

The Magnetic Field of a Finite Solenoid

NASA Technical Reports Server (NTRS)

Callaghan, Edmund E.; Maslen, Stephen H.

1960-01-01

The axial and radial fields at any point inside or outside a finite solenoid with infinitely thin walls are derived. Solution of the equations has been obtained in terms of tabulated complete elliptic integrals. For the axial field an accurate approximation is given in terms of elementary functions. Fields internal and external to the solenoid are presented in graphical form for a wide variety of solenoid lengths.

Impressed sources and fields in the volume-integral-equation formulation of electromagnetic scattering by a finite object: A tutorial

NASA Astrophysics Data System (ADS)

Mishchenko, Michael I.; Yurkin, Maxim A.

2018-07-01

Although free space cannot generate electromagnetic waves, the majority of existing accounts of frequency-domain electromagnetic scattering by particles and particle groups are based on the postulate of existence of an impressed incident field, usually in the form of a plane wave. In this tutorial we discuss how to account for the actual existence of impressed source currents rather than impressed incident fields. Specifically, we outline a self-consistent theoretical formalism describing electromagnetic scattering by an arbitrary finite object in the presence of arbitrarily distributed impressed currents, some of which can be far removed from the object and some can reside in its vicinity, including inside the object. To make the resulting formalism applicable to a wide range of scattering-object morphologies, we use the framework of the volume integral equation formulation of electromagnetic scattering, couple it with the notion of the transition operator, and exploit the fundamental symmetry property of this operator. Among novel results, this tutorial includes a streamlined proof of fundamental symmetry (reciprocity) relations, a simplified derivation of the Foldy equations, and an explicit analytical expression for the transition operator of a multi-component scattering object.

An analysis of the flow field near the fuel injection location in a gas core reactor.

NASA Technical Reports Server (NTRS)

Weinstein, H.; Murty, B. G. K.; Porter, R. W.

1971-01-01

An analytical study is presented which shows the effects of large energy release and the concurrent high acceleration of inner stream fluid on the coaxial flow field in a gas core reactor. The governing equations include the assumptions of only radial radiative transport of energy represented as an energy diffusion term in the Euler equations. The method of integral relations is used to obtain the numerical solution. Results show that the rapidly accelerating, heat generating inner stream actually shrinks in radius as it expands axially.

High altitude chemically reacting gas particle mixtures. Volume 1: A theoretical analysis and development of the numerical solution. [rocket nozzle and orbital plume flow fields

NASA Technical Reports Server (NTRS)

Smith, S. D.

1984-01-01

The overall contractual effort and the theory and numerical solution for the Reacting and Multi-Phase (RAMP2) computer code are described. The code can be used to model the dominant phenomena which affect the prediction of liquid and solid rocket nozzle and orbital plume flow fields. Fundamental equations for steady flow of reacting gas-particle mixtures, method of characteristics, mesh point construction, and numerical integration of the conservation equations are considered herein.

All-optical differential equation solver with constant-coefficient tunable based on a single microring resonator.

PubMed

Yang, Ting; Dong, Jianji; Lu, Liangjun; Zhou, Linjie; Zheng, Aoling; Zhang, Xinliang; Chen, Jianping

2014-07-04

Photonic integrated circuits for photonic computing open up the possibility for the realization of ultrahigh-speed and ultra wide-band signal processing with compact size and low power consumption. Differential equations model and govern fundamental physical phenomena and engineering systems in virtually any field of science and engineering, such as temperature diffusion processes, physical problems of motion subject to acceleration inputs and frictional forces, and the response of different resistor-capacitor circuits, etc. In this study, we experimentally demonstrate a feasible integrated scheme to solve first-order linear ordinary differential equation with constant-coefficient tunable based on a single silicon microring resonator. Besides, we analyze the impact of the chirp and pulse-width of input signals on the computing deviation. This device can be compatible with the electronic technology (typically complementary metal-oxide semiconductor technology), which may motivate the development of integrated photonic circuits for optical computing.

All-optical differential equation solver with constant-coefficient tunable based on a single microring resonator

PubMed Central

Yang, Ting; Dong, Jianji; Lu, Liangjun; Zhou, Linjie; Zheng, Aoling; Zhang, Xinliang; Chen, Jianping

2014-01-01

Photonic integrated circuits for photonic computing open up the possibility for the realization of ultrahigh-speed and ultra wide-band signal processing with compact size and low power consumption. Differential equations model and govern fundamental physical phenomena and engineering systems in virtually any field of science and engineering, such as temperature diffusion processes, physical problems of motion subject to acceleration inputs and frictional forces, and the response of different resistor-capacitor circuits, etc. In this study, we experimentally demonstrate a feasible integrated scheme to solve first-order linear ordinary differential equation with constant-coefficient tunable based on a single silicon microring resonator. Besides, we analyze the impact of the chirp and pulse-width of input signals on the computing deviation. This device can be compatible with the electronic technology (typically complementary metal-oxide semiconductor technology), which may motivate the development of integrated photonic circuits for optical computing. PMID:24993440

Gyrokinetic equations and full f solution method based on Dirac's constrained Hamiltonian and inverse Kruskal iteration

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heikkinen, J. A.; Nora, M.

2011-02-15

Gyrokinetic equations of motion, Poisson equation, and energy and momentum conservation laws are derived based on the reduced-phase-space Lagrangian and inverse Kruskal iteration introduced by Pfirsch and Correa-Restrepo [J. Plasma Phys. 70, 719 (2004)]. This formalism, together with the choice of the adiabatic invariant J= as one of the averaging coordinates in phase space, provides an alternative to the standard gyrokinetics. Within second order in gyrokinetic parameter, the new equations do not show explicit ponderomotivelike or polarizationlike terms. Pullback of particle information with an iterated gyrophase and field dependent gyroradius function from the gyrocenter position defined by gyroaveraged coordinates allowsmore » direct numerical integration of the gyrokinetic equations in particle simulation of the field and particles with full distribution function. As an example, gyrokinetic systems with polarization drift either present or absent in the equations of motion are considered.« less

An introduction to generalized functions with some applications in aerodynamics and aeroacoustics

NASA Technical Reports Server (NTRS)

Farassat, F.

1994-01-01

In this paper, we start with the definition of generalized functions as continuous linear functionals on the space of infinitely differentiable functions with compact support. The concept of generalization differentiation is introduced next. This is the most important concept in generalized function theory and the applications we present utilize mainly this concept. First, some of the results of classical analysis, such as Leibniz rule of differentiation under the integral sign and the divergence theorem, are derived using the generalized function theory. It is shown that the divergence theorem remains valid for discontinuous vector fields provided that the derivatives are all viewed as generalized derivatives. This implies that all conservation laws of fluid mechanics are valid as they stand for discontinuous fields with all derivatives treated as generalized deriatives. Once these derivatives are written as ordinary derivatives and jumps in the field parameters across discontinuities, the jump conditions can be easily found. For example, the unsteady shock jump conditions can be derived from mass and momentum conservation laws. By using a generalized function theory, this derivative becomes trivial. Other applications of the generalized function theory in aerodynamics discussed in this paper are derivation of general transport theorems for deriving governing equations of fluid mechanics, the interpretation of finite part of divergent integrals, derivation of Oswatiitsch integral equation of transonic flow, and analysis of velocity field discontinuities as sources of vorticity. Applications in aeroacoustics presented here include the derivation of the Kirchoff formula for moving surfaces,the noise from moving surfaces, and shock noise source strength based on the Ffowcs Williams-Hawkings equation.

Analytical solutions for avalanche-breakdown voltages of single-diffused Gaussian junctions

NASA Astrophysics Data System (ADS)

Shenai, K.; Lin, H. C.

1983-03-01

Closed-form solutions of the potential difference between the two edges of the depletion layer of a single diffused Gaussian p-n junction are obtained by integrating Poisson's equation and equating the magnitudes of the positive and negative charges in the depletion layer. By using the closed form solution of the static Poisson's equation and Fulop's average ionization coefficient, the ionization integral in the depletion layer is computed, which yields the correct values of avalanche breakdown voltage, depletion layer thickness at breakdown, and the peak electric field as a function of junction depth. Newton's method is used for rapid convergence. A flowchart to perform the calculations with a programmable hand-held calculator, such as the TI-59, is shown.

A boundary integral equation method using auxiliary interior surface approach for acoustic radiation and scattering in two dimensions.

PubMed

Yang, S A

2002-10-01

This paper presents an effective solution method for predicting acoustic radiation and scattering fields in two dimensions. The difficulty of the fictitious characteristic frequency is overcome by incorporating an auxiliary interior surface that satisfies certain boundary condition into the body surface. This process gives rise to a set of uniquely solvable boundary integral equations. Distributing monopoles with unknown strengths over the body and interior surfaces yields the simple source formulation. The modified boundary integral equations are further transformed to ordinary ones that contain nonsingular kernels only. This implementation allows direct application of standard quadrature formulas over the entire integration domain; that is, the collocation points are exactly the positions at which the integration points are located. Selecting the interior surface is an easy task. Moreover, only a few corresponding interior nodal points are sufficient for the computation. Numerical calculations consist of the acoustic radiation and scattering by acoustically hard elliptic and rectangular cylinders. Comparisons with analytical solutions are made. Numerical results demonstrate the efficiency and accuracy of the current solution method.

Sensitivity of rough differential equations: An approach through the Omega lemma

NASA Astrophysics Data System (ADS)

Coutin, Laure; Lejay, Antoine

2018-03-01

The Itô map gives the solution of a Rough Differential Equation, a generalization of an Ordinary Differential Equation driven by an irregular path, when existence and uniqueness hold. By studying how a path is transformed through the vector field which is integrated, we prove that the Itô map is Hölder or Lipschitz continuous with respect to all its parameters. This result unifies and weakens the hypotheses of the regularity results already established in the literature.

Exact dark soliton solutions for a family of N coupled nonlinear Schrödinger equations in optical fiber media.

PubMed

Nakkeeran, K

2001-10-01

We consider a family of N coupled nonlinear Schrödinger equations which govern the simultaneous propagation of N fields in the normal dispersion regime of an optical fiber with various important physical effects. The linear eigenvalue problem associated with the integrable form of all the equations is constructed with the help of the Ablowitz-Kaup-Newell-Segur method. Using the Hirota bilinear method, exact dark soliton solutions are explicitly derived.

Robust multiscale field-only formulation of electromagnetic scattering

NASA Astrophysics Data System (ADS)

Sun, Qiang; Klaseboer, Evert; Chan, Derek Y. C.

2017-01-01

We present a boundary integral formulation of electromagnetic scattering by homogeneous bodies that are characterized by linear constitutive equations in the frequency domain. By working with the Cartesian components of the electric E and magnetic H fields and with the scalar functions (r .E ) and (r .H ) where r is a position vector, the problem can be cast as having to solve a set of scalar Helmholtz equations for the field components that are coupled by the usual electromagnetic boundary conditions at material boundaries. This facilitates a direct solution for the surface values of E and H rather than having to work with surface currents or surface charge densities as intermediate quantities in existing methods. Consequently, our formulation is free of the well-known numerical instability that occurs in the zero-frequency or long-wavelength limit in traditional surface integral solutions of Maxwell's equations and our numerical results converge uniformly to the static results in the long-wavelength limit. Furthermore, we use a formulation of the scalar Helmholtz equation that is expressed as classically convergent integrals and does not require the evaluation of principal value integrals or any knowledge of the solid angle. Therefore, standard quadrature and higher order surface elements can readily be used to improve numerical precision for the same number of degrees of freedom. In addition, near and far field values can be calculated with equal precision, and multiscale problems in which the scatterers possess characteristic length scales that are both large and small relative to the wavelength can be easily accommodated. From this we obtain results for the scattering and transmission of electromagnetic waves at dielectric boundaries that are valid for any ratio of the local surface curvature to the wave number. This is a generalization of the familiar Fresnel formula and Snell's law, valid at planar dielectric boundaries, for the scattering and transmission of electromagnetic waves at surfaces of arbitrary curvature. Implementation details are illustrated with scattering by multiple perfect electric conductors as well as dielectric bodies with complex geometries and composition.

Introduction to the thermodynamic Bethe ansatz

NASA Astrophysics Data System (ADS)

van Tongeren, Stijn J.

2016-08-01

We give a pedagogical introduction to the thermodynamic Bethe ansatz, a method that allows us to describe the thermodynamics of integrable models whose spectrum is found via the (asymptotic) Bethe ansatz. We set the stage by deriving the Fermi-Dirac distribution and associated free energy of free electrons, and then in a similar though technically more complicated fashion treat the thermodynamics of integrable models, focusing first on the one-dimensional Bose gas with delta function interaction as a clean pedagogical example, secondly the XXX spin chain as an elementary (lattice) model with prototypical complicating features in the form of bound states, and finally the {SU}(2) chiral Gross-Neveu model as a field theory example. Throughout this discussion we emphasize the central role of particle and hole densities, whose relations determine the model under consideration. We then discuss tricks that allow us to use the same methods to describe the exact spectra of integrable field theories on a circle, in particular the chiral Gross-Neveu model. We moreover discuss the simplification of TBA equations to Y systems, including the transition back to integral equations given sufficient analyticity data, in simple examples.

Equation of state of the one- and three-dimensional Bose-Bose gases

NASA Astrophysics Data System (ADS)

Chiquillo, Emerson

2018-06-01

We calculate the equation of state of Bose-Bose gases in one and three dimensions in the framework of an effective quantum field theory. The beyond-mean-field approximation at zero temperature and the one-loop finite-temperature results are obtained performing functional integration on a local effective action. The ultraviolet divergent zero-point quantum fluctuations are removed by means of dimensional regularization. We derive the nonlinear Schrödinger equation to describe one- and three-dimensional Bose-Bose mixtures and solve it analytically in the one-dimensional scenario. This equation supports self-trapped brightlike solitonic droplets and self-trapped darklike solitons. At low temperature, we also find that the pressure and the number of particles of symmetric quantum droplets have a nontrivial dependence on the chemical potential and the difference between the intra- and the interspecies coupling constants.

Liouvillian integrability of gravitating static isothermal fluid spheres

NASA Astrophysics Data System (ADS)

Iacono, Roberto; Llibre, Jaume

2014-10-01

We examine the integrability properties of the Einstein field equations for static, spherically symmetric fluid spheres, complemented with an isothermal equation of state, ρ = np. In this case, Einstein's equations can be reduced to a nonlinear, autonomous second order ordinary differential equation (ODE) for m/R (m is the mass inside the radius R) that has been solved analytically only for n = -1 and n = -3, yielding the cosmological solutions by De Sitter and Einstein, respectively, and for n = -5, case for which the solution can be derived from the De Sitter's one using a symmetry of Einstein's equations. The solutions for these three cases are of Liouvillian type, since they can be expressed in terms of elementary functions. Here, we address the question of whether Liouvillian solutions can be obtained for other values of n. To do so, we transform the second order equation into an equivalent autonomous Lotka-Volterra quadratic polynomial differential system in {R}^2, and characterize the Liouvillian integrability of this system using Darboux theory. We find that the Lotka-Volterra system possesses Liouvillian first integrals for n = -1, -3, -5, which descend from the existence of invariant algebraic curves of degree one, and for n = -6, a new solvable case, associated to an invariant algebraic curve of higher degree (second). For any other value of n, eventual first integrals of the Lotka-Volterra system, and consequently of the second order ODE for the mass function must be non-Liouvillian. This makes the existence of other solutions of the isothermal fluid sphere problem with a Liouvillian metric quite unlikely.

Cavity equations for a positive- or negative-refraction-index material with electric and magnetic nonlinearities.

PubMed

Mártin, Daniel A; Hoyuelos, Miguel

2009-11-01

We study evolution equations for electric and magnetic field amplitudes in a ring cavity with plane mirrors. The cavity is filled with a positive or negative-refraction-index material with third-order effective electric and magnetic nonlinearities. Two coupled nonlinear equations for the electric and magnetic amplitudes are obtained. We prove that the description can be reduced to one Lugiato-Lefever equation with generalized coefficients. A stability analysis of the homogeneous solution, complemented with numerical integration, shows that any combination of the parameters should correspond to one of three characteristic behaviors.

The Cauchy problem for the Pavlov equation

NASA Astrophysics Data System (ADS)

Grinevich, P. G.; Santini, P. M.; Wu, D.

2015-10-01

Commutation of multidimensional vector fields leads to integrable nonlinear dispersionless PDEs that arise in various problems of mathematical physics and have been intensively studied in recent literature. This report aims to solve the scattering and inverse scattering problem for integrable dispersionless PDEs, recently introduced just at a formal level, concentrating on the prototypical example of the Pavlov equation, and to justify an existence theorem for global bounded solutions of the associated Cauchy problem with small data. An essential part of this work was made during the visit of the three authors to the Centro Internacional de Ciencias in Cuernavaca, Mexico in November-December 2012.

Photon emission from quark-gluon plasma out of equilibrium

NASA Astrophysics Data System (ADS)

Hauksson, Sigtryggur; Jeon, Sangyong; Gale, Charles

2018-01-01

The photon emission from a nonequilibrium quark-gluon plasma is analyzed. We derive an integral equation that describes photon production through quark-antiquark annihilation and quark bremsstrahlung. It includes coherence between different scattering sites, also known as the Landau-Pomeranchuk-Migdal effect. These leading-order processes are studied for the first time together in an out-of-equilibrium field theoretical treatment that enables the inclusion of viscous corrections to the calculation of electromagnetic emission rates. In the special case of an isotropic, viscous, plasma the integral equation only depends on three constants, which capture the nonequilibrium nature of the medium.

High speed propeller acoustics and aerodynamics - A boundary element approach

NASA Technical Reports Server (NTRS)

Farassat, F.; Myers, M. K.; Dunn, M. H.

1989-01-01

The Boundary Element Method (BEM) is applied in this paper to the problems of acoustics and aerodynamics of high speed propellers. The underlying theory is described based on the linearized Ffowcs Williams-Hawkings equation. The surface pressure on the blade is assumed unknown in the aerodynamic problem. It is obtained by solving a singular integral equation. The acoustic problem is then solved by moving the field point inside the fluid medium and evaluating some surface and line integrals. Thus the BEM provides a powerful technique in calculation of high speed propeller aerodynamics and acoustics.

A numerical study of electromagnetic scattering from ocean like surfaces

NASA Technical Reports Server (NTRS)

Lentz, R. R.

1972-01-01

The integral equations describing electromagnetic scattering from one dimensional conducting surfaces are formulated and numerical results are presented. The results are compared with those obtained using approximate methods such as physical optics, geometrical optics, and perturbation theory. The integral equation solutions show that the surface radius of curvature must be greater than 2.5 wavelengths for either the physical optics or geometric optics to give satisfactory results. It has also been shown that perturbation theory agrees with the exact fields as long as the root mean square surface roughness is less than one-tenth of a wavelength.

G-Strands on symmetric spaces

PubMed Central

2017-01-01

We study the G-strand equations that are extensions of the classical chiral model of particle physics in the particular setting of broken symmetries described by symmetric spaces. These equations are simple field theory models whose configuration space is a Lie group, or in this case a symmetric space. In this class of systems, we derive several models that are completely integrable on finite dimensional Lie group G, and we treat in more detail examples with symmetric space SU(2)/S1 and SO(4)/SO(3). The latter model simplifies to an apparently new integrable nine-dimensional system. We also study the G-strands on the infinite dimensional group of diffeomorphisms, which gives, together with the Sobolev norm, systems of 1+2 Camassa–Holm equations. The solutions of these equations on the complementary space related to the Witt algebra decomposition are the odd function solutions. PMID:28413343

The Feynman-Vernon Influence Functional Approach in QED

NASA Astrophysics Data System (ADS)

Biryukov, Alexander; Shleenkov, Mark

2016-10-01

In the path integral approach we describe evolution of interacting electromagnetic and fermionic fields by the use of density matrix formalism. The equation for density matrix and transitions probability for fermionic field is obtained as average of electromagnetic field influence functional. We obtain a formula for electromagnetic field influence functional calculating for its various initial and final state. We derive electromagnetic field influence functional when its initial and final states are vacuum. We present Lagrangian for relativistic fermionic field under influence of electromagnetic field vacuum.

FastMag: Fast micromagnetic simulator for complex magnetic structures (invited)

NASA Astrophysics Data System (ADS)

Chang, R.; Li, S.; Lubarda, M. V.; Livshitz, B.; Lomakin, V.

2011-04-01

A fast micromagnetic simulator (FastMag) for general problems is presented. FastMag solves the Landau-Lifshitz-Gilbert equation and can handle multiscale problems with a high computational efficiency. The simulator derives its high performance from efficient methods for evaluating the effective field and from implementations on massively parallel graphics processing unit (GPU) architectures. FastMag discretizes the computational domain into tetrahedral elements and therefore is highly flexible for general problems. The magnetostatic field is computed via the superposition principle for both volume and surface parts of the computational domain. This is accomplished by implementing efficient quadrature rules and analytical integration for overlapping elements in which the integral kernel is singular. Thus, discretized superposition integrals are computed using a nonuniform grid interpolation method, which evaluates the field from N sources at N collocated observers in O(N) operations. This approach allows handling objects of arbitrary shape, allows easily calculating of the field outside the magnetized domains, does not require solving a linear system of equations, and requires little memory. FastMag is implemented on GPUs with ?> GPU-central processing unit speed-ups of 2 orders of magnitude. Simulations are shown of a large array of magnetic dots and a recording head fully discretized down to the exchange length, with over a hundred million tetrahedral elements on an inexpensive desktop computer.

Numerical modeling of subsurface communication

NASA Astrophysics Data System (ADS)

Burke, G. J.; Dease, C. G.; Didwall, E. M.; Lytle, R. J.

1985-02-01

Techniques are described for numerical modeling of through-the-Earth communication. The basic problem considered is evaluation of the field at a surface or airborne station due to an antenna buried in the Earth. Equations are given for the field of a point source in a homogeneous or stratified earth. These expressions involve infinite integrals over wave number, sometimes known as Sommerfield integrals. Numerical techniques used for evaluating these integrals are outlined. The problem of determining the current on a real antenna in the Earth, including the effect of insulation, is considered. Results are included for the fields of a point source in homogeneous and stratified earths and the field of a finite insulated dipole. The results are for electromagnetic propagation in the ELF-VLF range, but the codes also can address propagation problems at higher frequencies.

Towards information-optimal simulation of partial differential equations.

PubMed

Leike, Reimar H; Enßlin, Torsten A

2018-03-01

Most simulation schemes for partial differential equations (PDEs) focus on minimizing a simple error norm of a discretized version of a field. This paper takes a fundamentally different approach; the discretized field is interpreted as data providing information about a real physical field that is unknown. This information is sought to be conserved by the scheme as the field evolves in time. Such an information theoretic approach to simulation was pursued before by information field dynamics (IFD). In this paper we work out the theory of IFD for nonlinear PDEs in a noiseless Gaussian approximation. The result is an action that can be minimized to obtain an information-optimal simulation scheme. It can be brought into a closed form using field operators to calculate the appearing Gaussian integrals. The resulting simulation schemes are tested numerically in two instances for the Burgers equation. Their accuracy surpasses finite-difference schemes on the same resolution. The IFD scheme, however, has to be correctly informed on the subgrid correlation structure. In certain limiting cases we recover well-known simulation schemes like spectral Fourier-Galerkin methods. We discuss implications of the approximations made.

Magnetic field homogeneity perturbations in finite Halbach dipole magnets.

PubMed

Turek, Krzysztof; Liszkowski, Piotr

2014-01-01

Halbach hollow cylinder dipole magnets of a low or relatively low aspect ratio attract considerable attention due to their applications, among others, in compact NMR and MRI systems for investigating small objects. However, a complete mathematical framework for the analysis of magnetic fields in these magnets has been developed only for their infinitely long precursors. In such a case the analysis is reduced to two-dimensions (2D). The paper details the analysis of the 3D magnetic field in the Halbach dipole cylinders of a finite length. The analysis is based on three equations in which the components of the magnetic flux density Bx, By and Bz are expanded to infinite power series of the radial coordinate r. The zeroth term in the series corresponds to a homogeneous magnetic field Bc, which is perturbed by the higher order terms due to a finite magnet length. This set of equations is supplemented with an equation for the field profile B(z) along the magnet axis, presented for the first time. It is demonstrated that the geometrical factors in the coefficients of particular powers of r, defined by intricate integrals are the coefficients of the Taylor expansion of the homogeneity profile (B(z)-Bc)/Bc. As a consequence, the components of B can be easily calculated with an arbitrary accuracy. In order to describe perturbations of the field due to segmentation, two additional equations are borrowed from the 2D theory. It is shown that the 2D approach to the perturbations generated by the segmentation can be applied to the 3D Halbach structures unless r is not too close to the inner radius of the cylinder ri. The mathematical framework presented in the paper was verified with great precision by computations of B by a highly accurate integration of the magnetostatic Coulomb law and utilized to analyze the inhomogeneity of the magnetic field in the magnet with the accuracy better than 1 ppm. Copyright © 2013 Elsevier Inc. All rights reserved.

Weyl relativity: a novel approach to Weyl's ideas

NASA Astrophysics Data System (ADS)

Barceló, Carlos; Carballo-Rubio, Raúl; Garay, Luis J.

2017-06-01

In this paper we revisit the motivation and construction of a unified theory of gravity and electromagnetism, following Weyl's insights regarding the appealing potential connection between the gauge invariance of electromagnetism and the conformal invariance of the gravitational field. We highlight that changing the local symmetry group of spacetime permits to construct a theory in which these two symmetries are combined into a putative gauge symmetry but with second-order field equations and non-trivial mass scales, unlike the original higher-order construction by Weyl. We prove that the gravitational field equations are equivalent to the (trace-free) Einstein field equations, ensuring their compatibility with known tests of general relativity. As a corollary, the effective cosmological constant is rendered radiatively stable due to Weyl invariance. A novel phenomenological consequence characteristic of this construction, potentially relevant for cosmological observations, is the existence of an energy scale below which effects associated with the non-integrability of spacetime distances, and an effective mass for the electromagnetic field, appear simultaneously (as dual manifestations of the use of Weyl connections). We explain how former criticisms against Weyl's ideas lose most of their power in its present reincarnation, which we refer to as Weyl relativity, as it represents a Weyl-invariant, unified description of both the Einstein and Maxwell field equations.

Weyl relativity: a novel approach to Weyl's ideas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barceló, Carlos; Carballo-Rubio, Raúl; Garay, Luis J., E-mail: carlos@iaa.es, E-mail: raul.carballo-rubio@uct.ac.za, E-mail: luisj.garay@ucm.es

In this paper we revisit the motivation and construction of a unified theory of gravity and electromagnetism, following Weyl's insights regarding the appealing potential connection between the gauge invariance of electromagnetism and the conformal invariance of the gravitational field. We highlight that changing the local symmetry group of spacetime permits to construct a theory in which these two symmetries are combined into a putative gauge symmetry but with second-order field equations and non-trivial mass scales, unlike the original higher-order construction by Weyl. We prove that the gravitational field equations are equivalent to the (trace-free) Einstein field equations, ensuring their compatibilitymore » with known tests of general relativity. As a corollary, the effective cosmological constant is rendered radiatively stable due to Weyl invariance. A novel phenomenological consequence characteristic of this construction, potentially relevant for cosmological observations, is the existence of an energy scale below which effects associated with the non-integrability of spacetime distances, and an effective mass for the electromagnetic field, appear simultaneously (as dual manifestations of the use of Weyl connections). We explain how former criticisms against Weyl's ideas lose most of their power in its present reincarnation, which we refer to as Weyl relativity, as it represents a Weyl-invariant, unified description of both the Einstein and Maxwell field equations.« less

Determination of constant-volume balloon capabilities for aeronautical research. [specifically measurement of atmospheric phenomena

NASA Technical Reports Server (NTRS)

Tatom, F. B.; King, R. L.

1977-01-01

The proper application of constant-volume balloons (CVB) for measurement of atmospheric phenomena was determined. And with the proper interpretation of the resulting data. A literature survey covering 176 references is included. the governing equations describing the three-dimensional motion of a CVB immersed in a flow field are developed. The flowfield model is periodic, three-dimensional, and nonhomogeneous, with mean translational motion. The balloon motion and flow field equations are cast into dimensionless form for greater generality, and certain significant dimensionless groups are identified. An alternate treatment of the balloon motion, based on first-order perturbation analysis, is also presented. A description of the digital computer program, BALLOON, used for numerically integrating the governing equations is provided.

Numerical Simulations for Landing Gear Noise Generation and Radiation

NASA Technical Reports Server (NTRS)

Morris, Philip J.; Long, Lyle N.

2002-01-01

Aerodynamic noise from a landing gear in a uniform flow is computed using the Ffowcs Williams -Hawkings (FW-H) equation. The time accurate flow data on the surface is obtained using a finite volume flow solver on an unstructured and. The Ffowcs Williams-Hawkings equation is solved using surface integrals over the landing gear surface and over a permeable surface away from the landing gear. Two geometric configurations are tested in order to assess the impact of two lateral struts on the sound level and directivity in the far-field. Predictions from the Ffowcs Williams-Hawkings code are compared with direct calculations by the flow solver at several observer locations inside the computational domain. The permeable Ffowcs Williams-Hawkings surface predictions match those of the flow solver in the near-field. Far-field noise calculations coincide for both integration surfaces. The increase in drag observed between the two landing gear configurations is reflected in the sound pressure level and directivity mainly in the streamwise direction.

TBIEM3D: A Computer Program for Predicting Ducted Fan Engine Noise. Version 1.1

NASA Technical Reports Server (NTRS)

Dunn, M. H.

1997-01-01

This document describes the usage of the ducted fan noise prediction program TBIEM3D (Thin duct - Boundary Integral Equation Method - 3 Dimensional). A scattering approach is adopted in which the acoustic pressure field is split into known incident and unknown scattered parts. The scattering of fan-generated noise by a finite length circular cylinder in a uniform flow field is considered. The fan noise is modeled by a collection of spinning point thrust dipoles. The program, based on a Boundary Integral Equation Method (BIEM), calculates circumferential modal coefficients of the acoustic pressure at user-specified field locations. The duct interior can be of the hard wall type or lined. The duct liner is axisymmetric, locally reactive, and can be uniform or axially segmented. TBIEM3D is written in the FORTRAN programming language. Input to TBIEM3D is minimal and consists of geometric and kinematic parameters. Discretization and numerical parameters are determined automatically by the code. Several examples are presented to demonstrate TBIEM3D capabilities.

Rapid analysis of scattering from periodic dielectric structures using accelerated Cartesian expansions

DOE PAGES

Baczewski, Andrew David; Miller, Nicholas C.; Shanker, Balasubramaniam

2012-03-22

Here, the analysis of fields in periodic dielectric structures arise in numerous applications of recent interest, ranging from photonic bandgap structures and plasmonically active nanostructures to metamaterials. To achieve an accurate representation of the fields in these structures using numerical methods, dense spatial discretization is required. This, in turn, affects the cost of analysis, particularly for integral-equation-based methods, for which traditional iterative methods require Ο(Ν 2) operations, Ν being the number of spatial degrees of freedom. In this paper, we introduce a method for the rapid solution of volumetric electric field integral equations used in the analysis of doubly periodicmore » dielectric structures. The crux of our method is the accelerated Cartesian expansion algorithm, which is used to evaluate the requisite potentials in Ο(Ν) cost. Results are provided that corroborate our claims of acceleration without compromising accuracy, as well as the application of our method to a number of compelling photonics applications.« less

2.5-D poroelastic wave modelling in double porosity media

NASA Astrophysics Data System (ADS)

Liu, Xu; Greenhalgh, Stewart; Wang, Yanghua

2011-09-01

To approximate seismic wave propagation in double porosity media, the 2.5-D governing equations of poroelastic waves are developed and numerically solved. The equations are obtained by taking a Fourier transform in the strike or medium-invariant direction over all of the field quantities in the 3-D governing equations. The new memory variables from the Zener model are suggested as a way to represent the sum of the convolution integrals for both the solid particle velocity and the macroscopic fluid flux in the governing equations. By application of the memory equations, the field quantities at every time step need not be stored. However, this approximation allows just two Zener relaxation times to represent the very complex double porosity and dual permeability attenuation mechanism, and thus reduce the difficulty. The 2.5-D governing equations are numerically solved by a time-splitting method for the non-stiff parts and an explicit fourth-order Runge-Kutta method for the time integration and a Fourier pseudospectral staggered-grid for handling the spatial derivative terms. The 2.5-D solution has the advantage of producing a 3-D wavefield (point source) for a 2-D model but is much more computationally efficient than the full 3-D solution. As an illustrative example, we firstly show the computed 2.5-D wavefields in a homogeneous single porosity model for which we reformulated an analytic solution. Results for a two-layer, water-saturated double porosity model and a laterally heterogeneous double porosity structure are also presented.

An asymptotic-preserving Lagrangian algorithm for the time-dependent anisotropic heat transport equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chacon, Luis; del-Castillo-Negrete, Diego; Hauck, Cory D.

2014-09-01

We propose a Lagrangian numerical algorithm for a time-dependent, anisotropic temperature transport equation in magnetized plasmas in the large guide field regime. The approach is based on an analytical integral formal solution of the parallel (i.e., along the magnetic field) transport equation with sources, and it is able to accommodate both local and non-local parallel heat flux closures. The numerical implementation is based on an operator-split formulation, with two straightforward steps: a perpendicular transport step (including sources), and a Lagrangian (field-line integral) parallel transport step. Algorithmically, the first step is amenable to the use of modern iterative methods, while themore » second step has a fixed cost per degree of freedom (and is therefore scalable). Accuracy-wise, the approach is free from the numerical pollution introduced by the discrete parallel transport term when the perpendicular to parallel transport coefficient ratio X ⊥ /X ∥ becomes arbitrarily small, and is shown to capture the correct limiting solution when ε = X⊥L 2 ∥/X1L 2 ⊥ → 0 (with L∥∙ L⊥ , the parallel and perpendicular diffusion length scales, respectively). Therefore, the approach is asymptotic-preserving. We demonstrate the capabilities of the scheme with several numerical experiments with varying magnetic field complexity in two dimensions, including the case of transport across a magnetic island.« less

The Acceleration of Charged Particles at a Spherical Shock Moving through an Irregular Magnetic Field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Giacalone, J.

We investigate the physics of charged-particle acceleration at spherical shocks moving into a uniform plasma containing a turbulent magnetic field with a uniform mean. This has applications to particle acceleration at astrophysical shocks, most notably, to supernovae blast waves. We numerically integrate the equations of motion of a large number of test protons moving under the influence of electric and magnetic fields determined from a kinematically defined plasma flow associated with a radially propagating blast wave. Distribution functions are determined from the positions and velocities of the protons. The unshocked plasma contains a magnetic field with a uniform mean andmore » an irregular component having a Kolmogorov-like power spectrum. The field inside the blast wave is determined from Maxwell’s equations. The angle between the average magnetic field and unit normal to the shock varies with position along its surface. It is quasi-perpendicular to the unit normal near the sphere’s equator, and quasi-parallel to it near the poles. We find that the highest intensities of particles, accelerated by the shock, are at the poles of the blast wave. The particles “collect” at the poles as they approximately adhere to magnetic field lines that move poleward from their initial encounter with the shock at the equator, as the shock expands. The field lines at the poles have been connected to the shock the longest. We also find that the highest-energy protons are initially accelerated near the equator or near the quasi-perpendicular portion of the shock, where the acceleration is more rapid.« less

A positivity preserving and conservative variational scheme for phase-field modeling of two-phase flows

NASA Astrophysics Data System (ADS)

Joshi, Vaibhav; Jaiman, Rajeev K.

2018-05-01

We present a positivity preserving variational scheme for the phase-field modeling of incompressible two-phase flows with high density ratio. The variational finite element technique relies on the Allen-Cahn phase-field equation for capturing the phase interface on a fixed Eulerian mesh with mass conservative and energy-stable discretization. The mass conservation is achieved by enforcing a Lagrange multiplier which has both temporal and spatial dependence on the underlying solution of the phase-field equation. To make the scheme energy-stable in a variational sense, we discretize the spatial part of the Lagrange multiplier in the phase-field equation by the mid-point approximation. The proposed variational technique is designed to reduce the spurious and unphysical oscillations in the solution while maintaining the second-order accuracy of both spatial and temporal discretizations. We integrate the Allen-Cahn phase-field equation with the incompressible Navier-Stokes equations for modeling a broad range of two-phase flow and fluid-fluid interface problems. The coupling of the implicit discretizations corresponding to the phase-field and the incompressible flow equations is achieved via nonlinear partitioned iterative procedure. Comparison of results between the standard linear stabilized finite element method and the present variational formulation shows a remarkable reduction of oscillations in the solution while retaining the boundedness of the phase-indicator field. We perform a standalone test to verify the accuracy and stability of the Allen-Cahn two-phase solver. We examine the convergence and accuracy properties of the coupled phase-field solver through the standard benchmarks of the Laplace-Young law and a sloshing tank problem. Two- and three-dimensional dam break problems are simulated to assess the capability of the phase-field solver for complex air-water interfaces involving topological changes on unstructured meshes. Finally, we demonstrate the phase-field solver for a practical offshore engineering application of wave-structure interaction.

The development of a three-dimensional partially elliptic flow computer program for combustor research

NASA Technical Reports Server (NTRS)

Pan, Y. S.

1978-01-01

A three dimensional, partially elliptic, computer program was developed. Without requiring three dimensional computer storage locations for all flow variables, the partially elliptic program is capable of predicting three dimensional combustor flow fields with large downstream effects. The program requires only slight increase of computer storage over the parabolic flow program from which it was developed. A finite difference formulation for a three dimensional, fully elliptic, turbulent, reacting, flow field was derived. Because of the negligible diffusion effects in the main flow direction in a supersonic combustor, the set of finite-difference equations can be reduced to a partially elliptic form. Only the pressure field was governed by an elliptic equation and requires three dimensional storage; all other dependent variables are governed by parabolic equations. A numerical procedure which combines a marching integration scheme with an iterative scheme for solving the elliptic pressure was adopted.

Measurement and numerical simulation of high intensity focused ultrasound field in water

NASA Astrophysics Data System (ADS)

Lee, Kang Il

2017-11-01

In the present study, the acoustic field of a high intensity focused ultrasound (HIFU) transducer in water was measured by using a commercially available needle hydrophone intended for HIFU use. To validate the results of hydrophone measurements, numerical simulations of HIFU fields were performed by integrating the axisymmetric Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation from the frequency-domain perspective with the help of a MATLAB-based software package developed for HIFU simulation. Quantitative values for the focal waveforms, the peak pressures, and the size of the focal spot were obtained in various regimes of linear, quasilinear, and nonlinear propagation up to the source pressure levels when the shock front was formed in the waveform. The numerical results with the HIFU simulator solving the KZK equation were compared with the experimental data and found to be in good agreement. This confirms that the numerical simulation based on the KZK equation is capable of capturing the nonlinear pressure field of therapeutic HIFU transducers well enough to make it suitable for HIFU treatment planning.

Gaussian-windowed frame based method of moments formulation of surface-integral-equation for extended apertures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shlivinski, A., E-mail: amirshli@ee.bgu.ac.il; Lomakin, V., E-mail: vlomakin@eng.ucsd.edu

2016-03-01

Scattering or coupling of electromagnetic beam-field at a surface discontinuity separating two homogeneous or inhomogeneous media with different propagation characteristics is formulated using surface integral equation, which are solved by the Method of Moments with the aid of the Gabor-based Gaussian window frame set of basis and testing functions. The application of the Gaussian window frame provides (i) a mathematically exact and robust tool for spatial-spectral phase-space formulation and analysis of the problem; (ii) a system of linear equations in a transmission-line like form relating mode-like wave objects of one medium with mode-like wave objects of the second medium; (iii)more » furthermore, an appropriate setting of the frame parameters yields mode-like wave objects that blend plane wave properties (as if solving in the spectral domain) with Green's function properties (as if solving in the spatial domain); and (iv) a representation of the scattered field with Gaussian-beam propagators that may be used in many large (in terms of wavelengths) systems.« less

Investigation of smoothness-increasing accuracy-conserving filters for improving streamline integration through discontinuous fields.

PubMed

Steffen, Michael; Curtis, Sean; Kirby, Robert M; Ryan, Jennifer K

2008-01-01

Streamline integration of fields produced by computational fluid mechanics simulations is a commonly used tool for the investigation and analysis of fluid flow phenomena. Integration is often accomplished through the application of ordinary differential equation (ODE) integrators--integrators whose error characteristics are predicated on the smoothness of the field through which the streamline is being integrated--smoothness which is not available at the inter-element level of finite volume and finite element data. Adaptive error control techniques are often used to ameliorate the challenge posed by inter-element discontinuities. As the root of the difficulties is the discontinuous nature of the data, we present a complementary approach of applying smoothness-enhancing accuracy-conserving filters to the data prior to streamline integration. We investigate whether such an approach applied to uniform quadrilateral discontinuous Galerkin (high-order finite volume) data can be used to augment current adaptive error control approaches. We discuss and demonstrate through numerical example the computational trade-offs exhibited when one applies such a strategy.

On the self-force in Bopp-Podolsky electrodynamics

NASA Astrophysics Data System (ADS)

Gratus, Jonathan; Perlick, Volker; Tucker, Robin W.

2015-10-01

In the classical vacuum Maxwell-Lorentz theory the self-force of a charged point particle is infinite. This makes classical mass renormalization necessary and, in the special relativistic domain, leads to the Abraham-Lorentz-Dirac equation of motion possessing unphysical run-away and pre-acceleration solutions. In this paper we investigate whether the higher-order modification of classical vacuum electrodynamics suggested by Bopp, Landé, Thomas and Podolsky in the 1940s, can provide a solution to this problem. Since the theory is linear, Green-function techniques enable one to write the field of a charged point particle on Minkowski spacetime as an integral over the particle’s history. By introducing the notion of timelike worldlines that are ‘bounded away from the backward light-cone’ we are able to prescribe criteria for the convergence of such integrals. We also exhibit a timelike worldline yielding singular fields on a lightlike hyperplane in spacetime. In this case the field is mildly singular at the event where the particle crosses the hyperplane. Even in the case when the Bopp-Podolsky field is bounded, it exhibits a directional discontinuity as one approaches the point particle. We describe a procedure for assigning a value to the field on the particle worldline which enables one to define a finite Lorentz self-force. This is explicitly derived leading to an integro-differential equation for the motion of the particle in an external electromagnetic field. We conclude that any worldline solutions to this equation belonging to the categories discussed in the paper have continuous four-velocities.

Exact solution of matricial Φ23 quantum field theory

NASA Astrophysics Data System (ADS)

Grosse, Harald; Sako, Akifumi; Wulkenhaar, Raimar

2017-12-01

We apply a recently developed method to exactly solve the Φ3 matrix model with covariance of a two-dimensional theory, also known as regularised Kontsevich model. Its correlation functions collectively describe graphs on a multi-punctured 2-sphere. We show how Ward-Takahashi identities and Schwinger-Dyson equations lead in a special large- N limit to integral equations that we solve exactly for all correlation functions. The solved model arises from noncommutative field theory in a special limit of strong deformation parameter. The limit defines ordinary 2D Schwinger functions which, however, do not satisfy reflection positivity.

Divergent conservation laws in hyperbolic thermoelasticity

NASA Astrophysics Data System (ADS)

Murashkin, E. V.; Radayev, Y. N.

2018-05-01

The present study is devoted to the problem of formulation of conservation laws in divergent form for hyperbolic thermoelastic continua. The field formalism is applied to study the problem. A natural density of thermoelastic action and the corresponding variational least action principle are formulated. A special form of the first variation of the action is employed to obtain 4-covariant divergent conservation laws. Differential field equations and constitutive laws are derived from a special form of the first variation of the action integral. The objectivity of constitutive equations is provided by the rotationally invariant forms of the Lagrangian employed.

New 2D dilaton gravity for nonsingular black holes

NASA Astrophysics Data System (ADS)

Kunstatter, Gabor; Maeda, Hideki; Taves, Tim

2016-05-01

We construct a two-dimensional action that is an extension of spherically symmetric Einstein-Lanczos-Lovelock (ELL) gravity. The action contains arbitrary functions of the areal radius and the norm squared of its gradient, but the field equations are second order and obey Birkhoff’s theorem. In complete analogy with spherically symmetric ELL gravity, the field equations admit the generalized Misner-Sharp mass as the first integral that determines the form of the vacuum solution. The arbitrary functions in the action allow for vacuum solutions that describe a larger class of interesting nonsingular black hole spacetimes than previously available.

Accurate expansion of cylindrical paraxial waves for its straightforward implementation in electromagnetic scattering

NASA Astrophysics Data System (ADS)

Naserpour, Mahin; Zapata-Rodríguez, Carlos J.

2018-01-01

The evaluation of vector wave fields can be accurately performed by means of diffraction integrals, differential equations and also series expansions. In this paper, a Bessel series expansion which basis relies on the exact solution of the Helmholtz equation in cylindrical coordinates is theoretically developed for the straightforward yet accurate description of low-numerical-aperture focal waves. The validity of this approach is confirmed by explicit application to Gaussian beams and apertured focused fields in the paraxial regime. Finally we discuss how our procedure can be favorably implemented in scattering problems.

Modified Einstein and Navier-Stokes Equations

NASA Astrophysics Data System (ADS)

Bulyzhenkov, I. É.

2018-05-01

The appearance of inertial rest mass-energy is associated with the kinematic slowing-down of time and with the vortex state of the elementary massive space with zero integral of its kinetic and potential energies. An analog of the Einstein equation is found for moving densities of a non-empty metric space in the concept of the Einstein-Infeld material field. The vector consequences of this tensor equation for a metric medium of overlapping elementary carriers of continuous mass-energies allow us to modify the Navier-Stokes equation under inertial motion of the matter of the nonlocal field in the nonrelativistic limit. The nonlocality of massenergy generates kinematic accelerations of feedback to Newtonian acceleration, which impedes asymptotic divergence of energy fluxes. Stabilization of inertial media by dynamic Bernoulli pressure corresponds to nonlocal self-organization of Einstein-Infeld non-empty space and invalidates Newtonian localization of masses in empty space.

Modified Einstein and Navier–Stokes Equations

NASA Astrophysics Data System (ADS)

Bulyzhenkov, I. É.

2018-05-01

The appearance of inertial rest mass-energy is associated with the kinematic slowing-down of time and with the vortex state of the elementary massive space with zero integral of its kinetic and potential energies. An analog of the Einstein equation is found for moving densities of a non-empty metric space in the concept of the Einstein-Infeld material field. The vector consequences of this tensor equation for a metric medium of overlapping elementary carriers of continuous mass-energies allow us to modify the Navier-Stokes equation under inertial motion of the matter of the nonlocal field in the nonrelativistic limit. The nonlocality of massenergy generates kinematic accelerations of feedback to Newtonian acceleration, which impedes asymptotic divergence of energy fluxes. Stabilization of inertial media by dynamic Bernoulli pressure corresponds to nonlocal self-organization of Einstein-Infeld non-empty space and invalidates Newtonian localization of masses in empty space.

MHD Modeling of the Solar Wind with Turbulence Transport and Heating

NASA Technical Reports Server (NTRS)

Goldstein, M. L.; Usmanov, A. V.; Matthaeus, W. H.; Breech, B.

2009-01-01

We have developed a magnetohydrodynamic model that describes the global axisymmetric steady-state structure of the solar wind near solar minimum with account for transport of small-scale turbulence associated heating. The Reynolds-averaged mass, momentum, induction, and energy equations for the large-scale solar wind flow are solved simultaneously with the turbulence transport equations in the region from 0.3 to 100 AU. The large-scale equations include subgrid-scale terms due to turbulence and the turbulence (small-scale) equations describe the effects of transport and (phenomenologically) dissipation of the MHD turbulence based on a few statistical parameters (turbulence energy, normalized cross-helicity, and correlation scale). The coupled set of equations is integrated numerically for a source dipole field on the Sun by a time-relaxation method in the corotating frame of reference. We present results on the plasma, magnetic field, and turbulence distributions throughout the heliosphere and on the role of the turbulence in the large-scale structure and temperature distribution in the solar wind.

A solution to neural field equations by a recurrent neural network method

NASA Astrophysics Data System (ADS)

Alharbi, Abir

2012-09-01

Neural field equations (NFE) are used to model the activity of neurons in the brain, it is introduced from a single neuron 'integrate-and-fire model' starting point. The neural continuum is spatially discretized for numerical studies, and the governing equations are modeled as a system of ordinary differential equations. In this article the recurrent neural network approach is used to solve this system of ODEs. This consists of a technique developed by combining the standard numerical method of finite-differences with the Hopfield neural network. The architecture of the net, energy function, updating equations, and algorithms are developed for the NFE model. A Hopfield Neural Network is then designed to minimize the energy function modeling the NFE. Results obtained from the Hopfield-finite-differences net show excellent performance in terms of accuracy and speed. The parallelism nature of the Hopfield approaches may make them easier to implement on fast parallel computers and give them the speed advantage over the traditional methods.

Boundary integral equation analysis for suspension of spheres in Stokes flow

NASA Astrophysics Data System (ADS)

Corona, Eduardo; Veerapaneni, Shravan

2018-06-01

We show that the standard boundary integral operators, defined on the unit sphere, for the Stokes equations diagonalize on a specific set of vector spherical harmonics and provide formulas for their spectra. We also derive analytical expressions for evaluating the operators away from the boundary. When two particle are located close to each other, we use a truncated series expansion to compute the hydrodynamic interaction. On the other hand, we use the standard spectrally accurate quadrature scheme to evaluate smooth integrals on the far-field, and accelerate the resulting discrete sums using the fast multipole method (FMM). We employ this discretization scheme to analyze several boundary integral formulations of interest including those arising in porous media flow, active matter and magneto-hydrodynamics of rigid particles. We provide numerical results verifying the accuracy and scaling of their evaluation.

Hamiltonian structure of real Monge - Ampère equations

NASA Astrophysics Data System (ADS)

Nutku, Y.

1996-06-01

The variational principle for the real homogeneous Monge - Ampère equation in two dimensions is shown to contain three arbitrary functions of four variables. There exist two different specializations of this variational principle where the Lagrangian is degenerate and furthermore contains an arbitrary function of two variables. The Hamiltonian formulation of these degenerate Lagrangian systems requires the use of Dirac's theory of constraints. As in the case of most completely integrable systems the constraints are second class and Dirac brackets directly yield the Hamiltonian operators. Thus the real homogeneous Monge - Ampère equation in two dimensions admits two classes of infinitely many Hamiltonian operators, namely a family of local, as well as another family non-local Hamiltonian operators and symplectic 2-forms which depend on arbitrary functions of two variables. The simplest non-local Hamiltonian operator corresponds to the Kac - Moody algebra of vector fields and functions on the unit circle. Hamiltonian operators that belong to either class are compatible with each other but between classes there is only one compatible pair. In the case of real Monge - Ampère equations with constant right-hand side this compatible pair is the only pair of Hamiltonian operators that survives. Then the complete integrability of all these real Monge - Ampère equations follows by Magri's theorem. Some of the remarkable properties we have obtained for the Hamiltonian structure of the real homogeneous Monge - Ampère equation in two dimensions turn out to be generic to the real homogeneous Monge - Ampère equation and the geodesic flow for the complex homogeneous Monge - Ampère equation in arbitrary number of dimensions. Hence among all integrable nonlinear evolution equations in one space and one time dimension, the real homogeneous Monge - Ampère equation is distinguished as one that retains its character as an integrable system in multiple dimensions.

AdS/CFT and local renormalization group with gauge fields

NASA Astrophysics Data System (ADS)

Kikuchi, Ken; Sakai, Tadakatsu

2016-03-01

We revisit a study of local renormalization group (RG) with background gauge fields incorporated using the AdS/CFT correspondence. Starting with a (d+1)-dimensional bulk gravity coupled to scalars and gauge fields, we derive a local RG equation from a flow equation by working in the Hamilton-Jacobi formulation of the bulk theory. The Gauss's law constraint associated with gauge symmetry plays an important role. RG flows of the background gauge fields are governed by vector β-functions, and some of their interesting properties are known to follow. We give a systematic rederivation of them on the basis of the flow equation. Fixing an ambiguity of local counterterms in such a manner that is natural from the viewpoint of the flow equation, we determine all the coefficients uniquely appearing in the trace of the stress tensor for d=4. A relation between a choice of schemes and a virial current is discussed. As a consistency check, these are found to satisfy the integrability conditions of local RG transformations. From these results, we are led to a proof of a holographic c-theorem by determining a full family of schemes where a trace anomaly coefficient is related with a holographic c-function.

A hybrid numerical technique for predicting the aerodynamic and acoustic fields of advanced turboprops

NASA Technical Reports Server (NTRS)

Homicz, G. F.; Moselle, J. R.

1985-01-01

A hybrid numerical procedure is presented for the prediction of the aerodynamic and acoustic performance of advanced turboprops. A hybrid scheme is proposed which in principle leads to a consistent simultaneous prediction of both fields. In the inner flow a finite difference method, the Approximate-Factorization Alternating-Direction-Implicit (ADI) scheme, is used to solve the nonlinear Euler equations. In the outer flow the linearized acoustic equations are solved via a Boundary-Integral Equation (BIE) method. The two solutions are iteratively matched across a fictitious interface in the flow so as to maintain continuity. At convergence the resulting aerodynamic load prediction will automatically satisfy the appropriate free-field boundary conditions at the edge of the finite difference grid, while the acoustic predictions will reflect the back-reaction of the radiated field on the magnitude of the loading source terms, as well as refractive effects in the inner flow. The equations and logic needed to match the two solutions are developed and the computer program implementing the procedure is described. Unfortunately, no converged solutions were obtained, due to unexpectedly large running times. The reasons for this are discussed and several means to alleviate the situation are suggested.

Stochastic Ocean Predictions with Dynamically-Orthogonal Primitive Equations

NASA Astrophysics Data System (ADS)

Subramani, D. N.; Haley, P., Jr.; Lermusiaux, P. F. J.

2017-12-01

The coastal ocean is a prime example of multiscale nonlinear fluid dynamics. Ocean fields in such regions are complex and intermittent with unstationary heterogeneous statistics. Due to the limited measurements, there are multiple sources of uncertainties, including the initial conditions, boundary conditions, forcing, parameters, and even the model parameterizations and equations themselves. For efficient and rigorous quantification and prediction of these uncertainities, the stochastic Dynamically Orthogonal (DO) PDEs for a primitive equation ocean modeling system with a nonlinear free-surface are derived and numerical schemes for their space-time integration are obtained. Detailed numerical studies with idealized-to-realistic regional ocean dynamics are completed. These include consistency checks for the numerical schemes and comparisons with ensemble realizations. As an illustrative example, we simulate the 4-d multiscale uncertainty in the Middle Atlantic/New York Bight region during the months of Jan to Mar 2017. To provide intitial conditions for the uncertainty subspace, uncertainties in the region were objectively analyzed using historical data. The DO primitive equations were subsequently integrated in space and time. The probability distribution function (pdf) of the ocean fields is compared to in-situ, remote sensing, and opportunity data collected during the coincident POSYDON experiment. Results show that our probabilistic predictions had skill and are 3- to 4- orders of magnitude faster than classic ensemble schemes.

Numerical simulation for flow and heat transfer to Carreau fluid with magnetic field effect: Dual nature study

NASA Astrophysics Data System (ADS)

Hashim; Khan, Masood; Alshomrani, Ali Saleh

2017-12-01

This article considers a realistic approach to examine the magnetohydrodynamics (MHD) flow of Carreau fluid induced by the shrinking sheet subject to the stagnation-point. This study also explores the impacts of non-linear thermal radiation on the heat transfer process. The governing equations of physical model are expressed as a system of partial differential equations and are transformed into non-linear ordinary differential equations by introducing local similarity variables. The economized equations of the problem are numerically integrated using the Runge-Kutta Fehlberg integration scheme. In this study, we explore the condition of existence, non-existence, uniqueness and dual nature for obtaining numerical solutions. It is found that the solutions may possess multiple natures, upper and lower branch, for a specific range of shrinking parameter. Results indicate that due to an increment in the magnetic parameter, range of shrinking parameter where a dual solution exists, increases. Further, strong magnetic field enhances the thickness of the momentum boundary layer in case of the second solution while for first solution it reduces. We further note that the fluid suction diminishes the fluid velocity and therefore the thickness of the hydrodynamic boundary layer decreases as well. A critical analysis with existing works is performed which shows that outcome are benchmarks with these works.

Numerical modeling of subsurface communication, revision 1

NASA Astrophysics Data System (ADS)

Burke, G. J.; Dease, C. G.; Didwall, E. M.; Lytle, R. J.

1985-08-01

Techniques are described for numerical modeling of through-the-Earth communication. The basic problem considered is evaluation of the field at a surface or airborne station due to an antenna buried in the earth. Equations are given for the field of a point source in a homogeneous or stratified Earth. These expressions involve infinite integrals over wave number, sometimes known as Sommerfeld integrals. Numerical techniques used for evaluating these integrals are outlined. The problem of determining the current on a real antenna in the Earth, including the effect of insulation, is considered. Results are included for the fields of a point source in homogeneous and stratified earths and the field of a finite insulated dipole. The results are for electromagnetic propagation in the ELF-VLF range, but the codes also can address propagation problems at higher frequencies.

Spheroidal Integral Equations for Geodetic Inversion of Geopotential Gradients

NASA Astrophysics Data System (ADS)

Novák, Pavel; Šprlák, Michal

2018-03-01

The static Earth's gravitational field has traditionally been described in geodesy and geophysics by the gravitational potential (geopotential for short), a scalar function of 3-D position. Although not directly observable, geopotential functionals such as its first- and second-order gradients are routinely measured by ground, airborne and/or satellite sensors. In geodesy, these observables are often used for recovery of the static geopotential at some simple reference surface approximating the actual Earth's surface. A generalized mathematical model is represented by a surface integral equation which originates in solving Dirichlet's boundary-value problem of the potential theory defined for the harmonic geopotential, spheroidal boundary and globally distributed gradient data. The mathematical model can be used for combining various geopotential gradients without necessity of their re-sampling or prior continuation in space. The model extends the apparatus of integral equations which results from solving boundary-value problems of the potential theory to all geopotential gradients observed by current ground, airborne and satellite sensors. Differences between spherical and spheroidal formulations of integral kernel functions of Green's kind are investigated. Estimated differences reach relative values at the level of 3% which demonstrates the significance of spheroidal approximation for flattened bodies such as the Earth. The observation model can be used for combined inversion of currently available geopotential gradients while exploring their spectral and stochastic characteristics. The model would be even more relevant to gravitational field modelling of other bodies in space with more pronounced spheroidal geometry than that of the Earth.

Numerical solution of stiff systems of ordinary differential equations with applications to electronic circuits

NASA Technical Reports Server (NTRS)

Rosenbaum, J. S.

1971-01-01

Systems of ordinary differential equations in which the magnitudes of the eigenvalues (or time constants) vary greatly are commonly called stiff. Such systems of equations arise in nuclear reactor kinetics, the flow of chemically reacting gas, dynamics, control theory, circuit analysis and other fields. The research reported develops an A-stable numerical integration technique for solving stiff systems of ordinary differential equations. The method, which is called the generalized trapezoidal rule, is a modification of the trapezoidal rule. However, the method is computationally more efficient than the trapezoidal rule when the solution of the almost-discontinuous segments is being calculated.

Exactly solvable relativistic model with the anomalous interaction

NASA Astrophysics Data System (ADS)

Ferraro, Elena; Messina, Antonino; Nikitin, A. G.

2010-04-01

A special class of Dirac-Pauli equations with time-like vector potentials of an external field is investigated. An exactly solvable relativistic model describing the anomalous interaction of a neutral Dirac fermion with a cylindrically symmetric external electromagnetic field is presented. The related external field is a superposition of the electric field generated by a charged infinite filament and the magnetic field generated by a straight line current. In the nonrelativistic approximation the considered model is reduced to the integrable Pron’ko-Stroganov model.

On the Debye-Hückel effect of electric screening

NASA Astrophysics Data System (ADS)

Campos, L. M. B. C.; Lau, F. J. P.

2014-07-01

The paper considers non-linear self-consistent electric potential equation (Sec. I), due to a cloud made of a single species of electric charges, satisfying a Boltzmann distribution law (Sec. II). Exact solutions are obtained in a simple logarithmic form, in three cases: (Sec. III) spherical radial symmetry; (Sec. IV) plane parallel symmetry; (Sec. V) a special case of azimuthal-cylindrical symmetry. All these solutions, and their transformations (Sec. VI), involve the Debye-Hückel radius; the latter was originally defined from a solution of the linearized self-consistent potential equation. Using an exact solution of the self-consistent potential equation, the distance at which the potential vanishes differs from the Debye-Hückel radius by a factor of √2 . The preceding (Secs. II-VI) simple logarithmic exact solutions of the self-consistent potential equations involve no arbitrary constants, and thus are special or singular integrals not the general integral. The general solution of the self-consistent potential equation is obtained in the plane parallel case (Sec. VII), and it involves two arbitrary constants that can be reduced to one via a translation (Sec. VIII). The plots of dimensionless potential (Figure 1), electric field (Figure 2), charge density (Figure 3), and total charge between ζ and infinity (Figure 4), versus distance normalized to Debye-Hückel radius ζ ≡ z/a, show that (Sec. IX) there is a continuum of solutions, ranging from a charge distribution concentrated inside the Debye-Hückel radius to one spread-out beyond it. The latter case leads to the limiting case of logarithmic potential, and stronger electric field; the former case, of very concentrated charge distribution, leads to a fratricide effect and weaker electric field.

On the Debye–Hückel effect of electric screening

DOE Office of Scientific and Technical Information (OSTI.GOV)

Campos, L. M. B. C.; Lau, F. J. P.

2014-07-15

The paper considers non-linear self-consistent electric potential equation (Sec. I), due to a cloud made of a single species of electric charges, satisfying a Boltzmann distribution law (Sec. II). Exact solutions are obtained in a simple logarithmic form, in three cases: (Sec. III) spherical radial symmetry; (Sec. IV) plane parallel symmetry; (Sec. V) a special case of azimuthal-cylindrical symmetry. All these solutions, and their transformations (Sec. VI), involve the Debye-Hückel radius; the latter was originally defined from a solution of the linearized self-consistent potential equation. Using an exact solution of the self-consistent potential equation, the distance at which the potentialmore » vanishes differs from the Debye-Hückel radius by a factor of √(2). The preceding (Secs. II–VI) simple logarithmic exact solutions of the self-consistent potential equations involve no arbitrary constants, and thus are special or singular integrals not the general integral. The general solution of the self-consistent potential equation is obtained in the plane parallel case (Sec. VII), and it involves two arbitrary constants that can be reduced to one via a translation (Sec. VIII). The plots of dimensionless potential (Figure 1), electric field (Figure 2), charge density (Figure 3), and total charge between ζ and infinity (Figure 4), versus distance normalized to Debye-Hückel radius ζ ≡ z/a, show that (Sec. IX) there is a continuum of solutions, ranging from a charge distribution concentrated inside the Debye-Hückel radius to one spread-out beyond it. The latter case leads to the limiting case of logarithmic potential, and stronger electric field; the former case, of very concentrated charge distribution, leads to a fratricide effect and weaker electric field.« less

Dynamics of weakly inhomogeneous oscillator populations: perturbation theory on top of Watanabe-Strogatz integrability

NASA Astrophysics Data System (ADS)

Vlasov, Vladimir; Rosenblum, Michael; Pikovsky, Arkady

2016-08-01

As has been shown by Watanabe and Strogatz (WS) (1993 Phys. Rev. Lett. 70 2391), a population of identical phase oscillators, sine-coupled to a common field, is a partially integrable system: for any ensemble size its dynamics reduce to equations for three collective variables. Here we develop a perturbation approach for weakly nonidentical ensembles. We calculate corrections to the WS dynamics for two types of perturbations: those due to a distribution of natural frequencies and of forcing terms, and those due to small white noise. We demonstrate that in both cases, the complex mean field for which the dynamical equations are written is close to the Kuramoto order parameter, up to the leading order in the perturbation. This supports the validity of the dynamical reduction suggested by Ott and Antonsen (2008 Chaos 18 037113) for weakly inhomogeneous populations.

A general low frequency acoustic radiation capability for NASTRAN

NASA Technical Reports Server (NTRS)

Everstine, G. C.; Henderson, F. M.; Schroeder, E. A.; Lipman, R. R.

1986-01-01

A new capability called NASHUA is described for calculating the radiated acoustic sound pressure field exterior to a harmonically-excited arbitrary submerged 3-D elastic structure. The surface fluid pressures and velocities are first calculated by coupling a NASTRAN finite element model of the structure with a discretized form of the Helmholtz surface integral equation for the exterior fluid. After the fluid impedance is calculated, most of the required matrix operations are performed using the general matrix manipulation package (DMAP) available in NASTRAN. Far field radiated pressures are then calculated from the surface solution using the Helmholtz exterior integral equation. Other output quantities include the maximum sound pressure levels in each of the three coordinate planes, the rms and average surface pressures and normal velocities, the total radiated power and the radiation efficiency. The overall approach is illustrated and validated using known analytic solutions for submerged spherical shells subjected to both uniform and nonuniform applied loads.

Torsion analysis of cracked circular bars actuated by a piezoelectric coating

NASA Astrophysics Data System (ADS)

Hassani, A. R.; Faal, R. T.

2016-12-01

This study presents a formulation for a bar with circular cross-section, coated by a piezoelectric layer and subjected to Saint-Venant torsion loading. The bar is weakened by a Volterra-type screw dislocation. First, with aid of the finite Fourier transform, the stress fields in the circular bar and the piezoelectric layer are obtained. The problem is then reduced to a set of singular integral equations with a Cauchy-type singularity. Unknown dislocation density is achieved by numerical solution of these integral equations. Numerical results are discussed, to reveal the effect of the piezoelectric layer on the reduction of the mechanical stress intensity factor in the bar.

Simulating nonlinear steady-state traveling waves on the falling liquid film entrained by a gas flow

NASA Astrophysics Data System (ADS)

Tsvelodub, O. Yu; Bocharov, A. A.

2017-09-01

The article is devoted to the simulation of nonlinear waves on a liquid film flowing under gravity in the known stress field at the interface. The paper studies nonlinear waves on a liquid film, flowing under the action of gravity in a known stress field at the interface. In the case of small Reynolds numbers the problem is reduced to the consideration of solutions of the nonlinear integral-differential equation for film thickness deviation from the undisturbed level. The periodic and soliton steady-state traveling solutions of this equation have been numerically found. The analysis of branching of new families of steady-state traveling solutions has been performed. In particular, it is shown that this model equation has solutions in the form of solitons-humps.

Estimates of the seasonal mean vertical velocity fields of the extratropical Northern Hemisphere

NASA Technical Reports Server (NTRS)

White, G. H.

1983-01-01

Indirect methods are employed to estimate the wintertime and summertime mean vertical velocity fields of the extratropical Northern Hemisphere and intercomparisons are made, together with comparisons with mean seasonal patterns of cloudiness and precipitation. Twice-daily NMC operational analyses produced general circulation statistics for 11 winters and 12 summers, permitting calculation of the seasonal NMC averages for 6 hr forecasts, solution of the omega equation, integration of continuity equation downward from 100 mb, and solution of the thermodynamic energy equation in the absence of diabatic heating. The methods all yielded similar vertical velocity patterns; however, the magnitude of the vertical velocities could not be calculated with great accuracy. Orography was concluded to have less of an effect in summer than in winter, when winds are stronger.

Direct localization of poles of a meromorphic function from measurements on an incomplete boundary

NASA Astrophysics Data System (ADS)

Nara, Takaaki; Ando, Shigeru

2010-01-01

This paper proposes an algebraic method to reconstruct the positions of multiple poles in a meromorphic function field from measurements on an arbitrary simple arc in it. A novel issue is the exactness of the algorithm depending on whether the arc is open or closed, and whether it encloses or does not enclose the poles. We first obtain a differential equation that can equivalently determine the meromorphic function field. From it, we derive linear equations that relate the elementary symmetric polynomials of the pole positions to weighted integrals of the field along the simple arc and end-point terms of the arc when it is an open one. Eliminating the end-point terms based on an appropriate choice of weighting functions and a combination of the linear equations, we obtain a simple system of linear equations for solving the elementary symmetric polynomials. We also show that our algorithm can be applied to a 2D electric impedance tomography problem. The effects of the proximity of the poles, the number of measurements and noise on the localization accuracy are numerically examined.

Investigation of viscous/inviscid interaction in transonic flow over airfoils with suction

NASA Technical Reports Server (NTRS)

Vemuru, C. S.; Tiwari, S. N.

1988-01-01

The viscous/inviscid interaction over transonic airfoils with and without suction is studied. The streamline angle at the edge of the boundary layer is used to couple the viscous and inviscid flows. The potential flow equations are solved for the inviscid flow field. In the shock region, the Euler equations are solved using the method of integral relations. For this, the potential flow solution is used as the initial and boundary conditions. An integral method is used to solve the laminar boundary-layer equations. Since both methods are integral methods, a continuous interaction is allowed between the outer inviscid flow region and the inner viscous flow region. To avoid the Goldstein singularity near the separation point the laminar boundary-layer equations are derived in an inverse form to obtain solution for the flows with small separations. The displacement thickness distribution is specified instead of the usual pressure distribution to solve the boundry-layer equations. The Euler equations are solved for the inviscid flow using the finite volume technique and the coupling is achieved by a surface transpiration model. A method is developed to apply a minimum amount of suction that is required to have an attached flow on the airfoil. The turbulent boundary layer equations are derived using the bi-logarithmic wall law for mass transfer. The results are found to be in good agreement with available experimental data and with the results of other computational methods.

Multiexponential models of (1+1)-dimensional dilaton gravity and Toda-Liouville integrable models

NASA Astrophysics Data System (ADS)

de Alfaro, V.; Filippov, A. T.

2010-01-01

We study general properties of a class of two-dimensional dilaton gravity (DG) theories with potentials containing several exponential terms. We isolate and thoroughly study a subclass of such theories in which the equations of motion reduce to Toda and Liouville equations. We show that the equation parameters must satisfy a certain constraint, which we find and solve for the most general multiexponential model. It follows from the constraint that integrable Toda equations in DG theories generally cannot appear without accompanying Liouville equations. The most difficult problem in the two-dimensional Toda-Liouville (TL) DG is to solve the energy and momentum constraints. We discuss this problem using the simplest examples and identify the main obstacles to solving it analytically. We then consider a subclass of integrable two-dimensional theories where scalar matter fields satisfy the Toda equations and the two-dimensional metric is trivial. We consider the simplest case in some detail. In this example, we show how to obtain the general solution. We also show how to simply derive wavelike solutions of general TL systems. In the DG theory, these solutions describe nonlinear waves coupled to gravity and also static states and cosmologies. For static states and cosmologies, we propose and study a more general one-dimensional TL model typically emerging in one-dimensional reductions of higher-dimensional gravity and supergravity theories. We especially attend to making the analytic structure of the solutions of the Toda equations as simple and transparent as possible.

Determination of welding residual stresses by inverse approach with eigenstrain formulations of boundary integral equation

NASA Astrophysics Data System (ADS)

Ma, Hang; Wang, Ying; Qin, Qing-Hua

2011-04-01

Based on the concept of eigenstrain, a straightforward computational model of the inverse approach is proposed for determining the residual stress field induced by welding using the eigenstrain formulations of boundary integral equations. The eigenstrains are approximately expressed in terms of low-order polynomials in the local area around welded zones. The domain integrals with polynomial eigenstrains are transformed into the boundary integrals to preserve the favourable features of the boundary-only discretization in the process of numerical solutions. The sensitivity matrices in the inverse approach for evaluating the eigenstrain fields are constructed by either the measured deformations (displacements) on the boundary or the measured stresses in the domain after welding over a number of selected measuring points, or by both the measured information. It shows from the numerical examples that the results of residual stresses from deformation measurements are always better than those from stress measurements but they are sensitive to the noises from experiments. The results from stress measurements can be improved by introducing a few deformation measuring points while reducing the number of points for stress measuring to reduce the cost since the measurement of deformation is easier than that of stresses in practice.

Non-LTE line formation in a magnetic field. I. Noncoherent scattering and true absorption

DOE Office of Scientific and Technical Information (OSTI.GOV)

Domke, H.; Staude, J.

1973-08-01

The formation of a Zeeman-multiplet by noncoherent scattering and true absorption in a Milne-- Eddington atmosphere is considered assuming a homogeneous magnetic field and complete depolarization of the atomic line levels. The transfer equation for the Stokes parameters is transformed into a scalar integral equation of the Wiener-- Hopf type which is solved by Sobolev's method in closed form. The influence of the magnetic field on the mean scattering number in an infinite medium is discussed. The solution of the line formation problem is obtained for a Planckian source fruction. This solution may be simplified by making the ''finite fieldmore » approximation'', which should be sufficiently accurate for practical purposes. (auth)« less

Alternative bi-Hamiltonian structures for WDVV equations of associativity

NASA Astrophysics Data System (ADS)

Kalayci, J.; Nutku, Y.

1998-01-01

The WDVV equations of associativity in two-dimensional topological field theory are completely integrable third-order Monge-Ampère equations which admit bi-Hamiltonian structure. The time variable plays a distinguished role in the discussion of Hamiltonian structure, whereas in the theory of WDVV equations none of the independent variables merits such a distinction. WDVV equations admit very different alternative Hamiltonian structures under different possible choices of the time variable, but all these various Hamiltonian formulations can be brought together in the framework of the covariant theory of symplectic structure. They can be identified as different components of the covariant Witten-Zuckerman symplectic 2-form current density where a variational formulation of the WDVV equation that leads to the Hamiltonian operator through the Dirac bracket is available.

Electromagnetic inverse scattering

NASA Technical Reports Server (NTRS)

Bojarski, N. N.

1972-01-01

A three-dimensional electromagnetic inverse scattering identity, based on the physical optics approximation, is developed for the monostatic scattered far field cross section of perfect conductors. Uniqueness of this inverse identity is proven. This identity requires complete scattering information for all frequencies and aspect angles. A nonsingular integral equation is developed for the arbitrary case of incomplete frequence and/or aspect angle scattering information. A general closed-form solution to this integral equation is developed, which yields the shape of the scatterer from such incomplete information. A specific practical radar solution is presented. The resolution of this solution is developed, yielding short-pulse target resolution radar system parameter equations. The special cases of two- and one-dimensional inverse scattering and the special case of a priori knowledge of scatterer symmetry are treated in some detail. The merits of this solution over the conventional radar imaging technique are discussed.

A new method for extending solutions to the self-similar relativistic magnetohydrodynamic equations for black hole outflows

NASA Astrophysics Data System (ADS)

Ceccobello, C.; Cavecchi, Y.; Heemskerk, M. H. M.; Markoff, S.; Polko, P.; Meier, D.

2018-02-01

The paradigm in which magnetic fields play a crucial role in launching/collimating outflows in many astrophysical objects continues to gain support. However, semi-analytical models including the effect of magnetic fields on the dynamics and morphology of jets are still missing due to the intrinsic difficulties in integrating the equations describing a collimated, relativistic flow in the presence of gravity. Only few solutions have been found so far, due to the highly non-linear character of the equations together with the need to blindly search for singularities. These numerical problems prevented a full exploration of the parameter space. We present a new integration scheme to solve r-self-similar, stationary, axisymmetric magnetohydrodynamic (MHD) equations describing collimated, relativistic outflows crossing smoothly all the singular points (Alfvén point and modified slow/fast points). For the first time, we are able to integrate from the disc mid-plane to downstream of the modified fast point. We discuss an ensemble of jet solutions, emphasizing trends and features that can be compared to observables. We present, for the first time with a semi-analytical MHD model, solutions showing counter-rotation of the jet for a substantial fraction of its extent. We find diverse jet configurations with bulk Lorentz factors up to 10 and potential sites for recollimation between 103 and 107 gravitational radii. Such extended coverage of the intervals of quantities, such as magnetic-to-thermal energy ratios at the base or the heights/widths of the recollimation region, makes our solutions suitable for application to many different systems where jets are launched.

Computation of oscillating airfoil flows with one- and two-equation turbulence models

NASA Technical Reports Server (NTRS)

Ekaterinaris, J. A.; Menter, F. R.

1994-01-01

The ability of one- and two-equation turbulence models to predict unsteady separated flows over airfoils is evaluated. An implicit, factorized, upwind-biased numerical scheme is used for the integration of the compressible, Reynolds-averaged Navier-Stokes equations. The turbulent eddy viscosity is obtained from the computed mean flowfield by integration of the turbulent field equations. One- and two-equation turbulence models are first tested for a separated airfoil flow at fixed angle of incidence. The same models are then applied to compute the unsteady flowfields about airfoils undergoing oscillatory motion at low subsonic Mach numbers. Experimental cases where the flow has been tripped at the leading-edge and where natural transition was allowed to occur naturally are considered. The more recently developed turbulence models capture the physics of unsteady separated flow significantly better than the standard kappa-epsilon and kappa-omega models. However, certain differences in the hysteresis effects are observed. For an untripped high-Reynolds-number flow, it was found necessary to take into account the leading-edge transitional flow region to capture the correct physical mechanism that leads to dynamic stall.

A differential equation for the Generalized Born radii.

PubMed

Fogolari, Federico; Corazza, Alessandra; Esposito, Gennaro

2013-06-28

The Generalized Born (GB) model offers a convenient way of representing electrostatics in complex macromolecules like proteins or nucleic acids. The computation of atomic GB radii is currently performed by different non-local approaches involving volume or surface integrals. Here we obtain a non-linear second-order partial differential equation for the Generalized Born radius, which may be solved using local iterative algorithms. The equation is derived under the assumption that the usual GB approximation to the reaction field obeys Laplace's equation. The equation admits as particular solutions the correct GB radii for the sphere and the plane. The tests performed on a set of 55 different proteins show an overall agreement with other reference GB models and "perfect" Poisson-Boltzmann based values.

Two-dimensional Euler and Navier-Stokes Time accurate simulations of fan rotor flows

NASA Technical Reports Server (NTRS)

Boretti, A. A.

1990-01-01

Two numerical methods are presented which describe the unsteady flow field in the blade-to-blade plane of an axial fan rotor. These methods solve the compressible, time-dependent, Euler and the compressible, turbulent, time-dependent, Navier-Stokes conservation equations for mass, momentum, and energy. The Navier-Stokes equations are written in Favre-averaged form and are closed with an approximate two-equation turbulence model with low Reynolds number and compressibility effects included. The unsteady aerodynamic component is obtained by superposing inflow or outflow unsteadiness to the steady conditions through time-dependent boundary conditions. The integration in space is performed by using a finite volume scheme, and the integration in time is performed by using k-stage Runge-Kutta schemes, k = 2,5. The numerical integration algorithm allows the reduction of the computational cost of an unsteady simulation involving high frequency disturbances in both CPU time and memory requirements. Less than 200 sec of CPU time are required to advance the Euler equations in a computational grid made up of about 2000 grid during 10,000 time steps on a CRAY Y-MP computer, with a required memory of less than 0.3 megawords.

Method of mechanical quadratures for solving singular integral equations of various types

NASA Astrophysics Data System (ADS)

Sahakyan, A. V.; Amirjanyan, H. A.

2018-04-01

The method of mechanical quadratures is proposed as a common approach intended for solving the integral equations defined on finite intervals and containing Cauchy-type singular integrals. This method can be used to solve singular integral equations of the first and second kind, equations with generalized kernel, weakly singular equations, and integro-differential equations. The quadrature rules for several different integrals represented through the same coefficients are presented. This allows one to reduce the integral equations containing integrals of different types to a system of linear algebraic equations.

A computer program for the simulation of heat and moisture flow in soils

NASA Technical Reports Server (NTRS)

Camillo, P.; Schmugge, T. J.

1981-01-01

A computer program that simulates the flow of heat and moisture in soils is described. The space-time dependence of temperature and moisture content is described by a set of diffusion-type partial differential equations. The simulator uses a predictor/corrector to numerically integrate them, giving wetness and temperature profiles as a function of time. The simulator was used to generate solutions to diffusion-type partial differential equations for which analytical solutions are known. These equations include both constant and variable diffusivities, and both flux and constant concentration boundary conditions. In all cases, the simulated and analytic solutions agreed to within the error bounds which were imposed on the integrator. Simulations of heat and moisture flow under actual field conditions were also performed. Ground truth data were used for the boundary conditions and soil transport properties. The qualitative agreement between simulated and measured profiles is an indication that the model equations are reasonably accurate representations of the physical processes involved.

Classical electromagnetic fields from quantum sources in heavy-ion collisions

NASA Astrophysics Data System (ADS)

Holliday, Robert; McCarty, Ryan; Peroutka, Balthazar; Tuchin, Kirill

2017-01-01

Electromagnetic fields are generated in high energy nuclear collisions by spectator valence protons. These fields are traditionally computed by integrating the Maxwell equations with point sources. One might expect that such an approach is valid at distances much larger than the proton size and thus such a classical approach should work well for almost the entire interaction region in the case of heavy nuclei. We argue that, in fact, the contrary is true: due to the quantum diffusion of the proton wave function, the classical approximation breaks down at distances of the order of the system size. We compute the electromagnetic field created by a charged particle described initially as a Gaussian wave packet of width 1 fm and evolving in vacuum according to the Klein-Gordon equation. We completely neglect the medium effects. We show that the dynamics, magnitude and even sign of the electromagnetic field created by classical and quantum sources are different.

Residual stresses in AM fabricated ball during a heating process

NASA Astrophysics Data System (ADS)

Burenin, A. A.; Murashkin, E. V.; Dats, E. P.

2018-05-01

The present study is devoted to the problem of residual stresses calculation in AM fabricated ball during heating. Strains of the ball are assumed to be small, which allows to use the apparatus of the theory of thermoelastoplastic akin to Prandtl and Reuss. The problem of the evolution of the field of residual stresses in the ball at a given temperature on its external border is solved. The heat conduction equation and the equilibrium equations may be independently integrated when the hypothesis of the insignificance of the coupled effects of thermal and mechanical processes is adopted. The fields of residual stresses and displacements are computed.

Partial differential equation models in the socio-economic sciences.

PubMed

Burger, Martin; Caffarelli, Luis; Markowich, Peter A

2014-11-13

Mathematical models based on partial differential equations (PDEs) have become an integral part of quantitative analysis in most branches of science and engineering, recently expanding also towards biomedicine and socio-economic sciences. The application of PDEs in the latter is a promising field, but widely quite open and leading to a variety of novel mathematical challenges. In this introductory article of the Theme Issue, we will provide an overview of the field and its recent boosting topics. Moreover, we will put the contributions to the Theme Issue in an appropriate perspective. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

Scattering from arbitrarily shaped microstrip patch antennas

NASA Technical Reports Server (NTRS)

Shively, David G.; Deshpande, Manohar D.; Cockrell, Capers R.

1992-01-01

The scattering properties of arbitrarily shaped microstrip patch antennas are examined. The electric field integral equation for a current element on a grounded dielectric slab is developed for a rectangular geometry based on Galerkin's technique with subdomain rooftop basis functions. A shape function is introduced that allows a rectangular grid approximation to the arbitrarily shaped patch. The incident field on the patch is expressed as a function of incidence angle theta(i), phi(i). The resulting system of equations is then solved for the unknown current modes on the patch, and the electromagnetic scattering is calculated for a given angle. Comparisons are made with other calculated results as well as with measurements.

Wave function for time-dependent harmonically confined electrons in a time-dependent electric field.

PubMed

Li, Yu-Qi; Pan, Xiao-Yin; Sahni, Viraht

2013-09-21

The many-body wave function of a system of interacting particles confined by a time-dependent harmonic potential and perturbed by a time-dependent spatially homogeneous electric field is derived via the Feynman path-integral method. The wave function is comprised of a phase factor times the solution to the unperturbed time-dependent Schrödinger equation with the latter being translated by a time-dependent value that satisfies the classical driven equation of motion. The wave function reduces to that of the Harmonic Potential Theorem wave function for the case of the time-independent harmonic confining potential.

Mean-force-field and mean-spherical approximations for the electric microfield distribution at a charged point in the charged-hard-particles fluid

NASA Astrophysics Data System (ADS)

Rosenfeld, Yaakov

1989-01-01

The linearized mean-force-field approximation, leading to a Gaussian distribution, provides an exact formal solution to the mean-spherical integral equation model for the electric microfield distribution at a charged point in the general charged-hard-particles fluid. Lado's explicit solution for plasmas immediately follows this general observation.

A new formulation of electromagnetic wave scattering using an on-surface radiation boundary condition approach

NASA Technical Reports Server (NTRS)

Kriegsmann, Gregory A.; Taflove, Allen; Umashankar, Koradar R.

1987-01-01

A new formulation of electromagnetic wave scattering by convex, two-dimensional conducting bodies is reported. This formulation, called the on-surface radiation condition (OSRC) approach, is based upon an expansion of the radiation condition applied directly on the surface of a scatterer. It is now shown that application of a suitable radiation condition directly on the surface of a convex conducting scatterer can lead to substantial simplification of the frequency-domain integral equation for the scattered field, which is reduced to just a line integral. For the transverse magnetic case, the integrand is known explicitly. For the transverse electric case, the integrand can be easily constructed by solving an ordinary differential equation around the scatterer surface contour. Examples are provided which show that OSRC yields computed near and far fields which approach the exact results for canonical shapes such as the circular cylinder, square cylinder, and strip. Electrical sizes for the examples are ka = 5 and ka = 10. The new OSRC formulation of scattering may present a useful alternative to present integral equation and uniform high-frequency approaches for convex cylinders larger than ka = 1. Structures with edges or corners can also be analyzed, although more work is needed to incorporate the physics of singular currents at these discontinuities. Convex dielectric structures can also be treated using OSRC.

An analytical theory of a scattering of radio waves on meteoric ionization - II. Solution of the integro-differential equation in case of backscatter

NASA Astrophysics Data System (ADS)

Pecina, P.

2016-12-01

The integro-differential equation for the polarization vector P inside the meteor trail, representing the analytical solution of the set of Maxwell equations, is solved for the case of backscattering of radio waves on meteoric ionization. The transversal and longitudinal dimensions of a typical meteor trail are small in comparison to the distances to both transmitter and receiver and so the phase factor appearing in the kernel of the integral equation is large and rapidly changing. This allows us to use the method of stationary phase to obtain an approximate solution of the integral equation for the scattered field and for the corresponding generalized radar equation. The final solution is obtained by expanding it into the complete set of Bessel functions, which results in solving a system of linear algebraic equations for the coefficients of the expansion. The time behaviour of the meteor echoes is then obtained using the generalized radar equation. Examples are given for values of the electron density spanning a range from underdense meteor echoes to overdense meteor echoes. We show that the time behaviour of overdense meteor echoes using this method is very different from the one obtained using purely numerical solutions of the Maxwell equations. Our results are in much better agreement with the observations performed e.g. by the Ondřejov radar.

Quantum to classical transition in quantum field theory

NASA Astrophysics Data System (ADS)

Lombardo, Fernando C.

1998-12-01

We study the quatum to classical transition process in the context of quantum field theory. Extending the influence functional formalism of Feynman and Vernon, we study the decoherence process for self-interacting quantum fields in flat space. We also use this formalism for arbitrary geometries to analyze the quantum to classical transition in quantum gravity. After summarizing the main results known for the quantum Brownian motion, we consider a self-interacting field theory in Minkowski spacetime. We compute a coarse grained effective action by integrating out the field modes with wavelength shorter than a critical value. From this effective action we obtain the evolution equation for the reduced density matrix (master equation). We compute the diffusion coefficients for this equation and analyze the decoherence induced on the long-wavelength modes. We generalize the results to the case of a conformally coupled scalar field in de Sitter spacetime. We show that the decoherence is effective as long as the critical wavelength is taken to be not shorter than the Hubble radius. On the other hand, we study the classical limit for scalar-tensorial models in two dimensions. We consider different couplings between the dilaton and the scalar field. We discuss the Hawking radiation process and, from an exact evaluation of the influence functional, we study the conditions by which decoherence ensures the validity of the semiclassical approximation in cosmological metrics. Finally we consider four dimensional models with massive scalar fields, arbitrary coupled to the geometry. We compute the Einstein-Langevin equations in order to study the effect of the fluctuations induced by the quantum fields on the classical geometry.

Development of Finite Elements for Two-Dimensional Structural Analysis Using the Integrated Force Method

NASA Technical Reports Server (NTRS)

Kaljevic, Igor; Patnaik, Surya N.; Hopkins, Dale A.

1996-01-01

The Integrated Force Method has been developed in recent years for the analysis of structural mechanics problems. This method treats all independent internal forces as unknown variables that can be calculated by simultaneously imposing equations of equilibrium and compatibility conditions. In this paper a finite element library for analyzing two-dimensional problems by the Integrated Force Method is presented. Triangular- and quadrilateral-shaped elements capable of modeling arbitrary domain configurations are presented. The element equilibrium and flexibility matrices are derived by discretizing the expressions for potential and complementary energies, respectively. The displacement and stress fields within the finite elements are independently approximated. The displacement field is interpolated as it is in the standard displacement method, and the stress field is approximated by using complete polynomials of the correct order. A procedure that uses the definitions of stress components in terms of an Airy stress function is developed to derive the stress interpolation polynomials. Such derived stress fields identically satisfy the equations of equilibrium. Moreover, the resulting element matrices are insensitive to the orientation of local coordinate systems. A method is devised to calculate the number of rigid body modes, and the present elements are shown to be free of spurious zero-energy modes. A number of example problems are solved by using the present library, and the results are compared with corresponding analytical solutions and with results from the standard displacement finite element method. The Integrated Force Method not only gives results that agree well with analytical and displacement method results but also outperforms the displacement method in stress calculations.

Efficient Approaches for Evaluating the Planar Microstrip Green's Function and its Applications to the Analysis of Microstrip Antennas.

NASA Astrophysics Data System (ADS)

Barkeshli, Sina

A relatively simple and efficient closed form asymptotic representation of the microstrip dyadic surface Green's function is developed. The large parameter in this asymptotic development is proportional to the lateral separation between the source and field points along the planar microstrip configuration. Surprisingly, this asymptotic solution remains accurate even for very small (almost two tenths of a wavelength) lateral separation of the source and field points. The present asymptotic Green's function will thus allow a very efficient calculation of the currents excited on microstrip antenna patches/feed lines and monolithic millimeter and microwave integrated circuit (MIMIC) elements based on a moment method (MM) solution of an integral equation for these currents. The kernal of the latter integral equation is the present asymptotic form of the microstrip Green's function. It is noted that the conventional Sommerfeld integral representation of the microstrip surface Green's function is very poorly convergent when used in this MM formulation. In addition, an efficient exact steepest descent path integral form employing a radially propagating representation of the microstrip dyadic Green's function is also derived which exhibits a relatively faster convergence when compared to the conventional Sommerfeld integral representation. The same steepest descent form could also be obtained by deforming the integration contour of the conventional Sommerfeld representation; however, the radially propagating integral representation exhibits better convergence properties for laterally separated source and field points even before the steepest descent path of integration is used. Numerical results based on the efficient closed form asymptotic solution for the microstrip surface Green's function developed in this work are presented for the mutual coupling between a pair of dipoles on a single layer grounded dielectric slab. The accuracy of the latter calculations is confirmed by comparison with results based on an exact integral representation for that Green's function.

Quantum field theory in the presence of a medium: Green's function expansions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kheirandish, Fardin; Salimi, Shahriar

2011-12-15

Starting from a Lagrangian and using functional-integration techniques, series expansions of Green's function of a real scalar field and electromagnetic field, in the presence of a medium, are obtained. The parameter of expansion in these series is the susceptibility function of the medium. Relativistic and nonrelativistic Langevin-type equations are derived. Series expansions for Lifshitz energy in finite temperature and for an arbitrary matter distribution are derived. Covariant formulations for both scalar and electromagnetic fields are introduced. Two illustrative examples are given.

The derivation of vector magnetic fields from Stokes profiles - Integral versus least squares fitting techniques

NASA Technical Reports Server (NTRS)

Ronan, R. S.; Mickey, D. L.; Orrall, F. Q.

1987-01-01

The results of two methods for deriving photospheric vector magnetic fields from the Zeeman effect, as observed in the Fe I line at 6302.5 A at high spectral resolution (45 mA), are compared. The first method does not take magnetooptical effects into account, but determines the vector magnetic field from the integral properties of the Stokes profiles. The second method is an iterative least-squares fitting technique which fits the observed Stokes profiles to the profiles predicted by the Unno-Rachkovsky solution to the radiative transfer equation. For sunspot fields above about 1500 gauss, the two methods are found to agree in derived azimuthal and inclination angles to within about + or - 20 deg.

Calculation of Impedance Matrix Inner Integral to Prescribed Precision for the Magnetic Field Integral Equation

DTIC Science & Technology

2012-07-19

calculation point (z’, w) gives the size of the smallest cubature that provides w SD at the point z’ Figure F.1. The graph of the function f in (F.9...77 Figure F.2. The graph of the function g in (F.10...77 Figure F.3. The graph of the function h in (F.13

The Coupling of Finite Element and Integral Equation Representations for Efficient Three-Dimensional Modeling of Electromagnetic Scattering and Radiation

NASA Technical Reports Server (NTRS)

Cwik, Tom; Zuffada, Cinzia; Jamnejad, Vahraz

1996-01-01

Finite element modeling has proven useful for accurtely simulating scattered or radiated fields from complex three-dimensional objects whose geometry varies on the scale of a fraction of a wavelength.

FLiT: a field line trace code for magnetic confinement devices

NASA Astrophysics Data System (ADS)

Innocente, P.; Lorenzini, R.; Terranova, D.; Zanca, P.

2017-04-01

This paper presents a field line tracing code (FLiT) developed to study particle and energy transport as well as other phenomena related to magnetic topology in reversed-field pinch (RFP) and tokamak experiments. The code computes magnetic field lines in toroidal geometry using curvilinear coordinates (r, ϑ, ϕ) and calculates the intersections of these field lines with specified planes. The code also computes the magnetic and thermal diffusivity due to stochastic magnetic field in the collisionless limit. Compared to Hamiltonian codes, there are no constraints on the magnetic field functional formulation, which allows the integration of whichever magnetic field is required. The code uses the magnetic field computed by solving the zeroth-order axisymmetric equilibrium and the Newcomb equation for the first-order helical perturbation matching the edge magnetic field measurements in toroidal geometry. Two algorithms are developed to integrate the field lines: one is a dedicated implementation of a first-order semi-implicit volume-preserving integration method, and the other is based on the Adams-Moulton predictor-corrector method. As expected, the volume-preserving algorithm is accurate in conserving divergence, but slow because the low integration order requires small amplitude steps. The second algorithm proves to be quite fast and it is able to integrate the field lines in many partially and fully stochastic configurations accurately. The code has already been used to study the core and edge magnetic topology of the RFX-mod device in both the reversed-field pinch and tokamak magnetic configurations.

SYNTHESIS OF NOVEL ALL-DIELECTRIC GRATING FILTERS USING GENETIC ALGORITHMS

NASA Technical Reports Server (NTRS)

Zuffada, Cinzia; Cwik, Tom; Ditchman, Christopher

1997-01-01

We are concerned with the design of inhomogeneous, all dielectric (lossless) periodic structures which act as filters. Dielectric filters made as stacks of inhomogeneous gratings and layers of materials are being used in optical technology, but are not common at microwave frequencies. The problem is then finding the periodic cell's geometric configuration and permittivity values which correspond to a specified reflectivity/transmittivity response as a function of frequency/illumination angle. This type of design can be thought of as an inverse-source problem, since it entails finding a distribution of sources which produce fields (or quantities derived from them) of given characteristics. Electromagnetic sources (electric and magnetic current densities) in a volume are related to the outside fields by a well known linear integral equation. Additionally, the sources are related to the fields inside the volume by a constitutive equation, involving the material properties. Then, the relationship linking the fields outside the source region to those inside is non-linear, in terms of material properties such as permittivity, permeability and conductivity. The solution of the non-linear inverse problem is cast here as a combination of two linear steps, by explicitly introducing the electromagnetic sources in the computational volume as a set of unknowns in addition to the material unknowns. This allows to solve for material parameters and related electric fields in the source volume which are consistent with Maxwell's equations. Solutions are obtained iteratively by decoupling the two steps. First, we invert for the permittivity only in the minimization of a cost function and second, given the materials, we find the corresponding electric fields through direct solution of the integral equation in the source volume. The sources thus computed are used to generate the far fields and the synthesized triter response. The cost function is obtained by calculating the deviation between the synthesized value of reflectivity/transmittivity and the desired one. Solution geometries for the periodic cell are sought as gratings (ensembles of columns of different heights and widths), or combinations of homogeneous layers of different dielectric materials and gratings. Hence the explicit unknowns of the inversion step are the material permittivities and the relative boundaries separating homogeneous parcels of the periodic cell.

Comment on: Accurate and fast numerical solution of Poisson s equation for arbitrary, space-filling Voronoi polyhedra: Near-field corrections revisited

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gonis, Antonios; Zhang, Xiaoguang

2012-01-01

This is a comment on the paper by Aftab Alam, Brian G. Wilson, and D. D. Johnson [1], proposing the solution of the near-field corrections (NFC s) problem for the Poisson equation for extended, e.g., space filling, charge densities. We point out that the problem considered by the authors can be simply avoided by means of performing certain integrals in a particular order, while their method does not address the genuine problem of NFC s that arises when the solution of the Poisson equation is attempted within multiple scattering theory. We also point out a flaw in their line ofmore » reasoning leading to the expression for the potential inside the bounding sphere of a cell that makes it inapplicable to certain geometries.« less

Comment on ``Accurate and fast numerical solution of Poisson's equation for arbitrary, space-filling Voronoi polyhedra: Near-field corrections revisited''

NASA Astrophysics Data System (ADS)

Gonis, A.; Zhang, X.-G.

2012-09-01

This is a Comment on the paper by Alam, Wilson, and Johnson [Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.84.205106 84, 205106 (2011)], proposing the solution of the near-field corrections (NFCs) problem for the Poisson equation for extended, e.g., space-filling charge densities. We point out that the problem considered by the authors can be simply avoided by means of performing certain integrals in a particular order, whereas, their method does not address the genuine problem of NFCs that arises when the solution of the Poisson equation is attempted within multiple-scattering theory. We also point out a flaw in their line of reasoning, leading to the expression for the potential inside the bounding sphere of a cell that makes it inapplicable for certain geometries.

Computation of nonlinear ultrasound fields using a linearized contrast source method.

PubMed

Verweij, Martin D; Demi, Libertario; van Dongen, Koen W A

2013-08-01

Nonlinear ultrasound is important in medical diagnostics because imaging of the higher harmonics improves resolution and reduces scattering artifacts. Second harmonic imaging is currently standard, and higher harmonic imaging is under investigation. The efficient development of novel imaging modalities and equipment requires accurate simulations of nonlinear wave fields in large volumes of realistic (lossy, inhomogeneous) media. The Iterative Nonlinear Contrast Source (INCS) method has been developed to deal with spatiotemporal domains measuring hundreds of wavelengths and periods. This full wave method considers the nonlinear term of the Westervelt equation as a nonlinear contrast source, and solves the equivalent integral equation via the Neumann iterative solution. Recently, the method has been extended with a contrast source that accounts for spatially varying attenuation. The current paper addresses the problem that the Neumann iterative solution converges badly for strong contrast sources. The remedy is linearization of the nonlinear contrast source, combined with application of more advanced methods for solving the resulting integral equation. Numerical results show that linearization in combination with a Bi-Conjugate Gradient Stabilized method allows the INCS method to deal with fairly strong, inhomogeneous attenuation, while the error due to the linearization can be eliminated by restarting the iterative scheme.

A multivariate variational objective analysis-assimilation method. Part 2: Case study results with and without satellite data

NASA Technical Reports Server (NTRS)

Achtemeier, Gary L.; Kidder, Stanley Q.; Scott, Robert W.

1988-01-01

The variational multivariate assimilation method described in a companion paper by Achtemeier and Ochs is applied to conventional and conventional plus satellite data. Ground-based and space-based meteorological data are weighted according to the respective measurement errors and blended into a data set that is a solution of numerical forms of the two nonlinear horizontal momentum equations, the hydrostatic equation, and an integrated continuity equation for a dry atmosphere. The analyses serve first, to evaluate the accuracy of the model, and second to contrast the analyses with and without satellite data. Evaluation criteria measure the extent to which: (1) the assimilated fields satisfy the dynamical constraints, (2) the assimilated fields depart from the observations, and (3) the assimilated fields are judged to be realistic through pattern analysis. The last criterion requires that the signs, magnitudes, and patterns of the hypersensitive vertical velocity and local tendencies of the horizontal velocity components be physically consistent with respect to the larger scale weather systems.

The behavior of plasma with an arbitrary degree of degeneracy of electron gas in the conductive layer

NASA Astrophysics Data System (ADS)

Latyshev, A. V.; Gordeeva, N. M.

2017-09-01

We obtain an analytic solution of the boundary problem for the behavior (fluctuations) of an electron plasma with an arbitrary degree of degeneracy of the electron gas in the conductive layer in an external electric field. We use the kinetic Vlasov-Boltzmann equation with the Bhatnagar-Gross-Krook collision integral and the Maxwell equation for the electric field. We use the mirror boundary conditions for the reflections of electrons from the layer boundary. The boundary problem reduces to a one-dimensional problem with a single velocity. For this, we use the method of consecutive approximations, linearization of the equations with respect to the absolute distribution of the Fermi-Dirac electrons, and the conservation law for the number of particles. Separation of variables then helps reduce the problem equations to a characteristic system of equations. In the space of generalized functions, we find the eigensolutions of the initial system, which correspond to the continuous spectrum (Van Kampen mode). Solving the dispersion equation, we then find the eigensolutions corresponding to the adjoint and discrete spectra (Drude and Debye modes). We then construct the general solution of the boundary problem by decomposing it into the eigensolutions. The coefficients of the decomposition are given by the boundary conditions. This allows obtaining the decompositions of the distribution function and the electric field in explicit form.

Simulation of bipolar charge transport in nanocomposite polymer films

NASA Astrophysics Data System (ADS)

Lean, Meng H.; Chu, Wei-Ping L.

2015-03-01

This paper describes 3D particle-in-cell simulation of bipolar charge injection and transport through nanocomposite film comprised of ferroelectric ceramic nanofillers in an amorphous polymer matrix. The classical electrical double layer (EDL) model for a monopolar core is extended (eEDL) to represent the nanofiller by replacing it with a dipolar core. Charge injection at the electrodes assumes metal-polymer Schottky emission at low to moderate fields and Fowler-Nordheim tunneling at high fields. Injected particles migrate via field-dependent Poole-Frenkel mobility and recombine with Monte Carlo selection. The simulation algorithm uses a boundary integral equation method for solution of the Poisson equation coupled with a second-order predictor-corrector scheme for robust time integration of the equations of motion. The stability criterion of the explicit algorithm conforms to the Courant-Friedrichs-Levy limit assuring robust and rapid convergence. The model is capable of simulating a wide dynamic range spanning leakage current to pre-breakdown. Simulation results for BaTiO3 nanofiller in amorphous polymer matrix indicate that charge transport behavior depend on nanoparticle polarization with anti-parallel orientation showing the highest leakage conduction and therefore lowest level of charge trapping in the interaction zone. Charge recombination is also highest, at the cost of reduced leakage conduction charge. The eEDL model predicts the meandering pathways of charge particle trajectories.

The development of the time dependence of the nuclear EMP electric field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Eng, C

The nuclear electromagnetic pulse (EMP) electric field calculated with the legacy code CHAP is compared with the field given by an integral solution of Maxwell's equations, also known as the Jefimenko equation, to aid our current understanding on the factors that affect the time dependence of the EMP. For a fair comparison the CHAP current density is used as a source in the Jefimenko equation. At first, the comparison is simplified by neglecting the conduction current and replacing the standard atmosphere with a constant density air slab. The simplicity of the resultant current density aids in determining the factors thatmore » affect the rise, peak and tail of the EMP electric field versus time. The three dimensional nature of the radiating source, i.e. sources off the line-of-sight, and the time dependence of the derivative of the current density with respect to time are found to play significant roles in shaping the EMP electric field time dependence. These results are found to hold even when the conduction current and the standard atmosphere are properly accounted for. Comparison of the CHAP electric field with the Jefimenko electric field offers a direct validation of the high-frequency/outgoing wave approximation.« less

Electromagnetic scattering and emission by a fixed multi-particle object in local thermal equilibrium: General formalism.

PubMed

Mishchenko, Michael I

2017-10-01

The majority of previous studies of the interaction of individual particles and multi-particle groups with electromagnetic field have focused on either elastic scattering in the presence of an external field or self-emission of electromagnetic radiation. In this paper we apply semi-classical fluctuational electrodynamics to address the ubiquitous scenario wherein a fixed particle or a fixed multi-particle group is exposed to an external quasi-polychromatic electromagnetic field as well as thermally emits its own electromagnetic radiation. We summarize the main relevant axioms of fluctuational electrodynamics, formulate in maximally rigorous mathematical terms the general scattering-emission problem for a fixed object, and derive such fundamental corollaries as the scattering-emission volume integral equation, the Lippmann-Schwinger equation for the dyadic transition operator, the multi-particle scattering-emission equations, and the far-field limit. We show that in the framework of fluctuational electrodynamics, the computation of the self-emitted component of the total field is completely separated from that of the elastically scattered field. The same is true of the computation of the emitted and elastically scattered components of quadratic/bilinear forms in the total electromagnetic field. These results pave the way to the practical computation of relevant optical observables.

Covariant Hamiltonian tetrad approach to numerical relativity

NASA Astrophysics Data System (ADS)

Hamilton, Andrew J. S.

2017-12-01

A Hamiltonian approach to the equations of general relativity is proposed using the powerful mathematical language of multivector-valued differential forms. In the approach, the gravitational coordinates are the 12 spatial components of the line interval (the vierbein) including their antisymmetric parts, and their 12 conjugate momenta. A feature of the proposed formalism is that it allows Lorentz gauge freedoms to be imposed on the Lorentz connections rather than on the vierbein, which may facilitate numerical integration in some challenging problems. The 40 Hamilton's equations comprise 12 +12 =24 equations of motion, ten constraint equations (first class constraints, which must be arranged on the initial hypersurface of constant time, but which are guaranteed thereafter by conservation laws), and six identities (second class constraints). The six identities define a trace-free spatial tensor that is the gravitational analog of the magnetic field of electromagnetism. If the gravitational magnetic field is promoted to an independent field satisfying its own equation of motion, then the system becomes the Wahlquist-Estabrook-Buchman-Bardeen (WEBB) system, which is known to be strongly hyperbolic. Some other approaches, including Arnowitt-Deser-Misner, Baumgarte-Shapiro-Shibata-Nakamura, WEBB, and loop quantum gravity, are translated into the language of multivector-valued forms, bringing out their underlying mathematical structure.

Acceleration of incremental-pressure-correction incompressible flow computations using a coarse-grid projection method

NASA Astrophysics Data System (ADS)

Kashefi, Ali; Staples, Anne

2016-11-01

Coarse grid projection (CGP) methodology is a novel multigrid method for systems involving decoupled nonlinear evolution equations and linear elliptic equations. The nonlinear equations are solved on a fine grid and the linear equations are solved on a corresponding coarsened grid. Mapping functions transfer data between the two grids. Here we propose a version of CGP for incompressible flow computations using incremental pressure correction methods, called IFEi-CGP (implicit-time-integration, finite-element, incremental coarse grid projection). Incremental pressure correction schemes solve Poisson's equation for an intermediate variable and not the pressure itself. This fact contributes to IFEi-CGP's efficiency in two ways. First, IFEi-CGP preserves the velocity field accuracy even for a high level of pressure field grid coarsening and thus significant speedup is achieved. Second, because incremental schemes reduce the errors that arise from boundaries with artificial homogenous Neumann conditions, CGP generates undamped flows for simulations with velocity Dirichlet boundary conditions. Comparisons of the data accuracy and CPU times for the incremental-CGP versus non-incremental-CGP computations are presented.

Finite-surface method for the Maxwell equations with corner singularities

NASA Technical Reports Server (NTRS)

Vinokur, Marcel; Yarrow, Maurice

1994-01-01

The finite-surface method for the two-dimensional Maxwell equations in generalized coordinates is extended to treat perfect conductor boundaries with sharp corners. Known singular forms of the grid and the electromagnetic fields in the neighborhood of each corner are used to obtain accurate approximations to the surface and line integrals appearing in the method. Numerical results are presented for a harmonic plane wave incident on a finite flat plate. Comparisons with exact solutions show good agreement.

Spacetimes with Killing tensors. [for Einstein-Maxwell fields with certain spinor indices

NASA Technical Reports Server (NTRS)

Hughston, L. P.; Sommers, P.

1973-01-01

The characteristics of the Killing equation and the Killing tensor are discussed. A conformal Killing tensor is of interest inasmuch as it gives rise to a quadratic first integral for null geodesic orbits. The Einstein-Maxwell equations are considered together with the Bianchi identity and the conformal Killing tensor. Two examples for the application of the considered relations are presented, giving attention to the charged Kerr solution and the charged C-metric.

Features of the Paired Soliton Interactions Within the Framework of the Gardner Equation

NASA Astrophysics Data System (ADS)

Shurgalina, E. G.

2018-02-01

We study the dynamics of the two-soliton interaction within the framework of a completely integrable model, namely, the Gardner equation with negative cubic nonlinearity, which admits the existence of a limiting soliton. The features of the soliton interaction with participation of a thick soliton are demonstrated. Special attention is paid to the nonlinear-interaction influence on the wave-field moments, which determine the skewness and the kurtosis in the theory of turbulence.

Integrable Time-Dependent Quantum Hamiltonians

NASA Astrophysics Data System (ADS)

Sinitsyn, Nikolai A.; Yuzbashyan, Emil A.; Chernyak, Vladimir Y.; Patra, Aniket; Sun, Chen

2018-05-01

We formulate a set of conditions under which the nonstationary Schrödinger equation with a time-dependent Hamiltonian is exactly solvable analytically. The main requirement is the existence of a non-Abelian gauge field with zero curvature in the space of system parameters. Known solvable multistate Landau-Zener models satisfy these conditions. Our method provides a strategy to incorporate time dependence into various quantum integrable models while maintaining their integrability. We also validate some prior conjectures, including the solution of the driven generalized Tavis-Cummings model.

Gluon scattering amplitudes from gauge/string duality and integrability

NASA Astrophysics Data System (ADS)

Satoh, Yuji

2014-06-01

We discuss the gluon scattering amplitudes of the four-dimensional maximally supersymmetric Yang-Mills theory. By the gauge/string duality, the amplitudes at strong coupling are given by the area of the minimal surfaces in anti-de Sitter space, which can be analyzed by a set of integral equations of the thermodynamic Bethe ansatz (TBA) type. By using the two-dimensional integrable models and conformal field theories underlying the TBA system, we derive analytic expansions of the amplitudes around certain kinematic configurations.

Computation of Sound Propagation by Boundary Element Method

NASA Technical Reports Server (NTRS)

Guo, Yueping

2005-01-01

This report documents the development of a Boundary Element Method (BEM) code for the computation of sound propagation in uniform mean flows. The basic formulation and implementation follow the standard BEM methodology; the convective wave equation and the boundary conditions on the surfaces of the bodies in the flow are formulated into an integral equation and the method of collocation is used to discretize this equation into a matrix equation to be solved numerically. New features discussed here include the formulation of the additional terms due to the effects of the mean flow and the treatment of the numerical singularities in the implementation by the method of collocation. The effects of mean flows introduce terms in the integral equation that contain the gradients of the unknown, which is undesirable if the gradients are treated as additional unknowns, greatly increasing the sizes of the matrix equation, or if numerical differentiation is used to approximate the gradients, introducing numerical error in the computation. It is shown that these terms can be reformulated in terms of the unknown itself, making the integral equation very similar to the case without mean flows and simple for numerical implementation. To avoid asymptotic analysis in the treatment of numerical singularities in the method of collocation, as is conventionally done, we perform the surface integrations in the integral equation by using sub-triangles so that the field point never coincide with the evaluation points on the surfaces. This simplifies the formulation and greatly facilitates the implementation. To validate the method and the code, three canonic problems are studied. They are respectively the sound scattering by a sphere, the sound reflection by a plate in uniform mean flows and the sound propagation over a hump of irregular shape in uniform flows. The first two have analytical solutions and the third is solved by the method of Computational Aeroacoustics (CAA), all of which are used to compare the BEM solutions. The comparisons show very good agreements and validate the accuracy of the BEM approach implemented here.

Wave propagation problem for a micropolar elastic waveguide

NASA Astrophysics Data System (ADS)

Kovalev, V. A.; Murashkin, E. V.; Radayev, Y. N.

2018-04-01

A propagation problem for coupled harmonic waves of translational displacements and microrotations along the axis of a long cylindrical waveguide is discussed at present study. Microrotations modeling is carried out within the linear micropolar elasticity frameworks. The mathematical model of the linear (or even nonlinear) micropolar elasticity is also expanded to a field theory model by variational least action integral and the least action principle. The governing coupled vector differential equations of the linear micropolar elasticity are given. The translational displacements and microrotations in the harmonic coupled wave are decomposed into potential and vortex parts. Calibrating equations providing simplification of the equations for the wave potentials are proposed. The coupled differential equations are then reduced to uncoupled ones and finally to the Helmholtz wave equations. The wave equations solutions for the translational and microrotational waves potentials are obtained for a high-frequency range.

Using EIGER for Antenna Design and Analysis

NASA Technical Reports Server (NTRS)

Champagne, Nathan J.; Khayat, Michael; Kennedy, Timothy F.; Fink, Patrick W.

2007-01-01

EIGER (Electromagnetic Interactions GenERalized) is a frequency-domain electromagnetics software package that is built upon a flexible framework, designed using object-oriented techniques. The analysis methods used include moment method solutions of integral equations, finite element solutions of partial differential equations, and combinations thereof. The framework design permits new analysis techniques (boundary conditions, Green#s functions, etc.) to be added to the software suite with a sensible effort. The code has been designed to execute (in serial or parallel) on a wide variety of platforms from Intel-based PCs and Unix-based workstations. Recently, new potential integration scheme s that avoid singularity extraction techniques have been added for integral equation analysis. These new integration schemes are required for facilitating the use of higher-order elements and basis functions. Higher-order elements are better able to model geometrical curvature using fewer elements than when using linear elements. Higher-order basis functions are beneficial for simulating structures with rapidly varying fields or currents. Results presented here will demonstrate curren t and future capabilities of EIGER with respect to analysis of installed antenna system performance in support of NASA#s mission of exploration. Examples include antenna coupling within an enclosed environment and antenna analysis on electrically large manned space vehicles.

A modeling approach to predict acoustic nonlinear field generated by a transmitter with an aluminum lens.

PubMed

Fan, Tingbo; Liu, Zhenbo; Chen, Tao; Li, Faqi; Zhang, Dong

2011-09-01

In this work, the authors propose a modeling approach to compute the nonlinear acoustic field generated by a flat piston transmitter with an attached aluminum lens. In this approach, the geometrical parameters (radius and focal length) of a virtual source are initially determined by Snell's refraction law and then adjusted based on the Rayleigh integral result in the linear case. Then, this virtual source is used with the nonlinear spheroidal beam equation (SBE) model to predict the nonlinear acoustic field in the focal region. To examine the validity of this approach, the calculated nonlinear result is compared with those from the Westervelt and (Khokhlov-Zabolotskaya-Kuznetsov) KZK equations for a focal intensity of 7 kW/cm(2). Results indicate that this approach could accurately describe the nonlinear acoustic field in the focal region with less computation time. The proposed modeling approach is shown to accurately describe the nonlinear acoustic field in the focal region. Compared with the Westervelt equation, the computation time of this approach is significantly reduced. It might also be applicable for the widely used concave focused transmitter with a large aperture angle.

Absorbing Boundary Conditions in Quantum Relativistic Mechanics for Spinless Particles Subject to a Classical Electromagnetic Field

NASA Astrophysics Data System (ADS)

Sater, Julien

The theory of Artificial Boundary Conditions described by Antoine et al. [2,4-6] for the Schrodinger equation is applied to the Klein-Gordon (KG) in two-dimensions (2-D) for spinless particles subject to electromagnetic fields. We begin by providing definitions for a basic understanding of the theory of operators, differential geometry and wave front sets needed to discuss the factorization theorem thanks to Nirenberg and Hormander [14, 16]. The laser-free Klein-Gordon equation in 1-D is then discussed, followed by the case including electrodynamics potentials, concluding with the KG equation in 2-D space with electrodynamics potentials. We then consider numerical simulations of the laser-particle KG equation, which includes a brief analysis of a finite difference scheme. The conclusion integrates a discussion of the numerical results, the successful completion of the objective set forth, a declaration of the unanswered encountered questions and a suggestion of subjects for further research.

Global boundary flattening transforms for acoustic propagation under rough sea surfaces.

PubMed

Oba, Roger M

2010-07-01

This paper introduces a conformal transform of an acoustic domain under a one-dimensional, rough sea surface onto a domain with a flat top. This non-perturbative transform can include many hundreds of wavelengths of the surface variation. The resulting two-dimensional, flat-topped domain allows direct application of any existing, acoustic propagation model of the Helmholtz or wave equation using transformed sound speeds. Such a transform-model combination applies where the surface particle velocity is much slower than sound speed, such that the boundary motion can be neglected. Once the acoustic field is computed, the bijective (one-to-one and onto) mapping permits the field interpolation in terms of the original coordinates. The Bergstrom method for inverse Riemann maps determines the transform by iterated solution of an integral equation for a surface matching term. Rough sea surface forward scatter test cases provide verification of the method using a particular parabolic equation model of the Helmholtz equation.

Chiral higher spin theories and self-duality

NASA Astrophysics Data System (ADS)

Ponomarev, Dmitry

2017-12-01

We study recently proposed chiral higher spin theories — cubic theories of interacting massless higher spin fields in four-dimensional flat space. We show that they are naturally associated with gauge algebras, which manifest themselves in several related ways. Firstly, the chiral higher spin equations of motion can be reformulated as the self-dual Yang-Mills equations with the associated gauge algebras instead of the usual colour gauge algebra. We also demonstrate that the chiral higher spin field equations, similarly to the self-dual Yang-Mills equations, feature an infinite algebra of hidden symmetries, which ensures their integrability. Secondly, we show that off-shell amplitudes in chiral higher spin theories satisfy the generalised BCJ relations with the usual colour structure constants replaced by the structure constants of higher spin gauge algebras. We also propose generalised double copy procedures featuring higher spin theory amplitudes. Finally, using the light-cone deformation procedure we prove that the structure of the Lagrangian that leads to all these properties is universal and follows from Lorentz invariance.

Benchmark calculations of nonconservative charged-particle swarms in dc electric and magnetic fields crossed at arbitrary angles.

PubMed

Dujko, S; White, R D; Petrović, Z Lj; Robson, R E

2010-04-01

A multiterm solution of the Boltzmann equation has been developed and used to calculate transport coefficients of charged-particle swarms in gases under the influence of electric and magnetic fields crossed at arbitrary angles when nonconservative collisions are present. The hierarchy resulting from a spherical-harmonic decomposition of the Boltzmann equation in the hydrodynamic regime is solved numerically by representing the speed dependence of the phase-space distribution function in terms of an expansion in Sonine polynomials about a Maxwellian velocity distribution at an internally determined temperature. Results are given for electron swarms in certain collisional models for ionization and attachment over a range of angles between the fields and field strengths. The implicit and explicit effects of ionization and attachment on the electron-transport coefficients are considered using physical arguments. It is found that the difference between the two sets of transport coefficients, bulk and flux, resulting from the explicit effects of nonconservative collisions, can be controlled either by the variation in the magnetic field strengths or by the angles between the fields. In addition, it is shown that the phenomena of ionization cooling and/or attachment cooling/heating previously reported for dc electric fields carry over directly to the crossed electric and magnetic fields. The results of the Boltzmann equation analysis are compared with those obtained by a Monte Carlo simulation technique. The comparison confirms the theoretical basis and numerical integrity of the moment method for solving the Boltzmann equation and gives a set of well-established data that can be used to test future codes and plasma models.

Integrable time-dependent Hamiltonians, solvable Landau-Zener models and Gaudin magnets

NASA Astrophysics Data System (ADS)

Yuzbashyan, Emil A.

2018-05-01

We solve the non-stationary Schrödinger equation for several time-dependent Hamiltonians, such as the BCS Hamiltonian with an interaction strength inversely proportional to time, periodically driven BCS and linearly driven inhomogeneous Dicke models as well as various multi-level Landau-Zener tunneling models. The latter are Demkov-Osherov, bow-tie, and generalized bow-tie models. We show that these Landau-Zener problems and their certain interacting many-body generalizations map to Gaudin magnets in a magnetic field. Moreover, we demonstrate that the time-dependent Schrödinger equation for the above models has a similar structure and is integrable with a similar technique as Knizhnik-Zamolodchikov equations. We also discuss applications of our results to the problem of molecular production in an atomic Fermi gas swept through a Feshbach resonance and to the evaluation of the Landau-Zener transition probabilities.

MOM3D method of moments code theory manual

NASA Technical Reports Server (NTRS)

Shaeffer, John F.

1992-01-01

MOM3D is a FORTRAN algorithm that solves Maxwell's equations as expressed via the electric field integral equation for the electromagnetic response of open or closed three dimensional surfaces modeled with triangle patches. Two joined triangles (couples) form the vector current unknowns for the surface. Boundary conditions are for perfectly conducting or resistive surfaces. The impedance matrix represents the fundamental electromagnetic interaction of the body with itself. A variety of electromagnetic analysis options are possible once the impedance matrix is computed including backscatter radar cross section (RCS), bistatic RCS, antenna pattern prediction for user specified body voltage excitation ports, RCS image projection showing RCS scattering center locations, surface currents excited on the body as induced by specified plane wave excitation, and near field computation for the electric field on or near the body.

Cartan symmetries and global dynamical systems analysis in a higher-order modified teleparallel theory

NASA Astrophysics Data System (ADS)

Karpathopoulos, L.; Basilakos, S.; Leon, G.; Paliathanasis, A.; Tsamparlis, M.

2018-07-01

In a higher-order modified teleparallel theory cosmological we present analytical cosmological solutions. In particular we determine forms of the unknown potential which drives the scalar field such that the field equations form a Liouville integrable system. For the determination of the conservation laws we apply the Cartan symmetries. Furthermore, inspired from our solutions, a toy model is studied and it is shown that it can describe the Supernova data, while at the same time introduces dark matter components in the Hubble function. When the extra matter source is a stiff fluid then we show how analytical solutions for Bianchi I universes can be constructed from our analysis. Finally, we perform a global dynamical analysis of the field equations by using variables different from that of the Hubble-normalization.

PREFACE Integrability and nonlinear phenomena Integrability and nonlinear phenomena

NASA Astrophysics Data System (ADS)

Gómez-Ullate, David; Lombardo, Sara; Mañas, Manuel; Mazzocco, Marta; Nijhoff, Frank; Sommacal, Matteo

2010-10-01

Back in 1967, Clifford Gardner, John Greene, Martin Kruskal and Robert Miura published a seminal paper in Physical Review Letters which was to become a cornerstone in the theory of integrable systems. In 2006, the authors of this paper received the AMS Steele Prize. In this award the AMS pointed out that `In applications of mathematics, solitons and their descendants (kinks, anti-kinks, instantons, and breathers) have entered and changed such diverse fields as nonlinear optics, plasma physics, and ocean, atmospheric, and planetary sciences. Nonlinearity has undergone a revolution: from a nuisance to be eliminated, to a new tool to be exploited.' From this discovery the modern theory of integrability bloomed, leading scientists to a deep understanding of many nonlinear phenomena which is by no means reachable by perturbation methods or other previous tools from linear theories. Nonlinear phenomena appear everywhere in nature, their description and understanding is therefore of great interest both from the theoretical and applicative point of view. If a nonlinear phenomenon can be represented by an integrable system then we have at our disposal a variety of tools to achieve a better mathematical description of the phenomenon. This special issue is largely dedicated to investigations of nonlinear phenomena which are related to the concept of integrability, either involving integrable systems themselves or because they use techniques from the theory of integrability. The idea of this special issue originated during the 18th edition of the Nonlinear Evolution Equations and Dynamical Systems (NEEDS) workshop, held at Isola Rossa, Sardinia, Italy, 16-23 May 2009 (http://needs-conferences.net/2009/). The issue benefits from the occasion offered by the meeting, in particular by its mini-workshops programme, and contains invited review papers and contributed papers. It is worth pointing out that there was an open call for papers and all contributions were peer reviewed according to the standards of the journal. The selection of papers in this issue aims to bring together recent developments and findings, even though it consists of only a fraction of the impressive developments in recent years which have affected a broad range of fields, including the theory of special functions, quantum integrable systems, numerical analysis, cellular automata, representations of quantum groups, symmetries of difference equations, discrete geometry, among others. The special issue begins with four review papers: Integrable models in nonlinear optics and soliton solutions Degasperis [1] reviews integrable models in nonlinear optics. He presents a number of approximate models which are integrable and illustrates the links between the mathematical and applicative aspects of the theory of integrable dynamical systems. In particular he discusses the recent impact of boomeronic-type wave equations on applications arising in the context of the resonant interaction of three waves. Hamiltonian PDEs: deformations, integrability, solutions Dubrovin [2] presents classification results for systems of nonlinear Hamiltonian partial differential equations (PDEs) in one spatial dimension. In particular he uses a perturbative approach to the theory of integrability of these systems and discusses their solutions. He conjectures universality of the critical behaviour for the solutions, where the notion of universality refers to asymptotic independence of the structure of solutions (at the point of gradient catastrophe) from the choice of generic initial data as well as from the choice of a generic PDE. KP solitons in shallow water Kodama [3] presents a survey of recent studies on soliton solutions of the Kadomtsev-Petviashvili (KP) equation. A large variety of exact soliton solutions of the KP equation are presented and classified. The study includes numerical analysis of the stability of the found solution as well as numerical simulations of the initial value problems which indicate that a certain class of initial waves approach asymptotically these exact solutions of the KP equation. The author discusses an application of the theory to the problem of the resonant interaction of solitary waves appearing in the reflection of an obliquely incident wave onto a vertical wall, known as the Mach reflection problem in shallow water. A beautiful explanation of the problem was presented in a swimming pool experiment during NEEDS 2009. Smooth and peaked solitons of the CH equation Holm and Ivanov [4] discuss the relations between smooth and peaked soliton solutions for the Camassa-Holm (CH) shallow water wave equation in one spatial dimension. They first present the derivation of the soliton solution for the CH equation by means of inverse scattering transform (IST); the solution is obtained in a form that admits the peakon limit. The canonical Hamiltonian formulation of the CH equation in action-angle variables is recovered using the scattering data. The authors review some of the geometric properties of the CH equation and conclude their review with the higher dimensional generalization of the dispersionless CH equation, known as EPDiff. They also consider the possible extensions of their approach in three open problems. Regular contributions to this issue cover a wide range of topics related to integrable systems. Let us briefly illustrate some of the topics covered by this issue. One of the main topics is the study of hierarchies of integrable equations. The multifaceted idea of integrability of a particular PDE includes an approach whose aim is to find an infinite set of independent conserved quantities, much in the spirit of Liouville integrability in classical mechanics. The existence of these conserved quantities in involution, or of the corresponding infinite set of commuting symmetries, leads to an infinite set of commuting flows; i.e., to the construction of a hierarchy of compatible PDEs with respect to an infinite set of times. Obviously one can generalize or adapt this construction to different settings like the integro-differential, discrete or super-symmetric ones. The emphasis is usually to find auxiliary linear systems defining an infinite set of linear commuting flows whose solutions, if some asymptotic conditions are imposed, are named wave or Baker-Akhiezer functions. These linear flows determine the so called Lax equations, another infinite set of commuting equations whose compatibility leads to the so called Zakharov-Shabat system. An alternative description of the hierarchies is achieved with the use of the bilinear equations directly linked with the tau-function description of the hierarchy. There are two paradigmatic integrable hierarchies, namely the KP and 2-dimensional Toda lattice (2DTL). These hierarchies are treated within this volume in three contributions. In particular, Takasaki [5] reconsiders the extended Toda hierarchy of Carlet, Dubrovin and Zhang in the light of Ogawa's 2 + 1D extension of the 1D Toda hierarchy. It turns out that the former may be thought of as some sort of dimensional reduction of the latter. This explains the structure of the bilinear formalism proposed by Milanov. Carlet and Manas [6] study the 2-component KP and 2D Toda hierarchies and solve explicitly several implicit constraints present in the usual Lax formulation of the hierarchy, thus identifying a set of free dependent variables for such hierarchies. Finally, the KP hierarchy is considered in the paper by Lin et al [7], which explores the extended flows of a q-deformed modified KP hierarchy leading to the introduction of self-consistent sources. By a combination of the dressing method and the method of variation of constants, the authors are able through a dressing approach to find a scheme for the construction of solutions of the corresponding integrable equations with self-consistent sources. The study of dispersionless integrable hierarchies is an active field of research, and this special issue includes two papers devoted to the subject. Konopelchenko et al [8] describe critical and degenerate critical points of a scalar function which obeys the Euler-Poisson-Darboux equation in terms of the hodograph solutions of the dispersionless coupled Korteweg-de Vries hierarchies. Finally, Bogdanov [9] considers 2-component integrable generalizations of the dispersionless 2D Toda lattice hierarchy connected with non-Hamiltonian vector fields, similar to the Manakov-Santini hierarchy generalizing the dKP hierarchy. He presents the simplest 2-component generalization of the dispersionless 2DTL equation, being its differential reduction analogous to the Dunajski interpolating system. Some papers in the issue are concerned with methods to construct solutions of integrable systems, while others place more emphasis on studying properties of specific solutions of applicative interest. Among the first approach, the paper by Kaup and van Gorder [10] describes perturbation theory applied to the Inverse Scattering Transform in 3x eigenvalue problems of Zakharov-Shabat's type. Schiebold [11] studies a projection method to construct solutions of the Ablowitz-Kaup-Newell-Segur (AKNS) system, which enables her to write explicit N-soliton solutions in closed form. An example of the second kind is the paper by Biondini and Wang [12], who study in detail the behaviour of line soliton solutions of the 2DTL, describing their directions and amplitudes and also the richness of their interactions, which include resonant soliton interactions and web structure. An important field of study in integrable systems relates to the singularity structure of the solutions to nonlinear equations. When all movable singularities are poles, the system is said to have the Painleve property. The solutions may be multivalued but they can be analytically continued to meromorphic functions on the universal cover of the punctured Riemann sphere (the punctures being the fixed singularities) and the spectral curve is an affine algebraic curve. Benes and Previato [13] study the connection between the Painleve property and algebras of differential operators, extending an approach initiated by Flaschka. Solutions to some integrable systems can be constructed in terms of analytic objects associated to a spectral algebraic curve. It is therefore of interest to study the Riemann surfaces of algebraic functions, a program illustrated in the paper by Braden and Northover [14], who have implemented some algorithms for this purpose in a popular symbolic computation software. In the paper by Zhilinski [15], the critical points of the energy momentum map in classical Hamiltonian problems with nontrivial monodromy are shown to form regular lattices. The quantum mechanical counterpart has similar lattices for the joint spectrum of the commuting observables. Some examples are given in which these points form special geometric patterns. Claeys [16] uses analytic techniques and Riemann-Hilbert problems to study the asymptotic behaviour when x and t tend to infinity of a solution to the second member of the Painleve I hierarchy, which arises in multicritical string model theory and random matrix theory. This solution is conjectured to describe the universal asymptotics for Hamiltonian perturbations of hyperbolic equations near the point of gradient catastrophe for the unperturbed equation. Darboux and Backlund transformations were born more than a century ago in the context of the geometric theory of surfaces. In the past few decades they have become a useful element in the theory of integrability, with applications in different guises. Typically, they appear in dressing methods that show how to construct new interesting solutions from known simple ones. A few of the contributed papers to the issue make use of these transformations as one of their fundamental objects. Liu et al [17] use iterated Darboux transformations to construct compact representations of the multi-soliton solutions to the derivative nonlinear Schroedinger (DNLS) equation. Ragnisco and Zullo [18] construct Backlund transformations for the trigonometric classical Gaudin magnet in the partially anisotropic (xxz) case, identifying the subcase of transformations that preserve the real character of the variables. The recently discovered exceptional polynomials are complete polynomial systems that satisfy Sturm-Liouville problems but differ from the classical families of Hermite, Laguerre and Jacobi. Gomez-Ullate et al [19] prove that the families of exceptional orthogonal polynomials known to date can be obtained from the classical ones via a Darboux transformation, which becomes a useful tool to derive some of their properties. Integrability in the context of classical mechanics is associated to the existence of a sufficient number of conserved quantities, which allows sometimes an explicit integration of the equations of motion. This is the case for the motion of the Chaplygin sleigh, a rigid body motion on a fluid with nonholonomic constraints studied in the paper by Fedorov and Garcia-Naranjo [20], who derive explicit solutions and study their asymptotic behaviour. In connection with classical mechanics, some techniques of KAM theory have been used by Procesi [21] to derive normal forms for the NLS equation in its Hamiltonian formulation and prove existence and stability of quasi-periodic solutions in the case of periodic boundary conditions. Algebraic and group theoretic aspects of integrability are covered in a number of papers in the issue. The quest for symmetries of a system of differential equations usually allows us to reduce the order or the number of equations or to find special solutions possesing that symmetry, but algebraic aspects of integrable systems encompass a wide and rich spectrum of techniques, as evidenced by the following contributions. Muriel and Romero [22] perform a systematic study of all second order nonlinear ODEs that are linearizable by generalized Sundman and point transformations, showing that the two classes are inequivalent and providing an explicit characterization thereof. Lie algebras are also prominent in the work of Gerdjikov et al [23], where a class of integrable PDEs associated to symmetric spaces is studied in detail. In their approach, systems of nonlinear integrable PDEs are obtained as reductions of generic integrable systems corresponding to Lax operators with matrix coefficients. The reduction here is carried out using a reduction group which reflects symmetries of the Lax operator. These symmetries allow also a characterization of the corresponding Riemann-Hilbert data. Habibullin [24] employs algebraic techniques to study discrete chains of differential-difference equations that are Darboux integrable, i.e. that admit a certain number of nontrivial first integrals. Musso [25] provides a unified algebraic framework for the rational, trigonometric and elliptic Gaudin models. The results are achieved using a generalization of the Gaudin algebras and of the so-called coproduct method. Odesskii and Sokolov [26] present a classification of all infinite (1+1)-dimensional hydrodynamic-type chains of shift one. They establish a one-to-one correspondence between integrable chains and infinite triangular Gibbons-Tsarev (GT) systems and thus reduce the classification problem to a description of all GT-systems. In Korff's paper [27] we find a study of various algebraic and combinatorial structures that emerge in the statistical vertex model with infinite spin, an integrable model associated to a certain quantum affine algebra. In the crystal limit, this model is connected with the WZNW model in conformal field theory. The motivation for some of the submitted contributions arises also from field theories in theoretical physics. Ferreira et al [28] construct soliton solutions with non-zero topological charges to the Skyrme-Faddeev model in Yang-Mills theory. Using techniques of differential geometry and complex analysis, Manton and Rink [29] explore vortex solutions on hyperbolic surfaces extending an approach by Witten. These solutions can be interpreted as self-dual SU(2) Yang-Mills fields on R4. Shah and Woodhouse [30] use the Penrose-Ward correspondence from twistor theory to relate generalized anti self-duality equations to certain isomonodromic problems whose solutions are expressed in terms of generalized hypergeometric functions. Applications of integrable systems and nonlinear phenomena in other fields are also present in some of the papers. Kanna et al [31] study the collision of soliton solutions to coherently coupled NLS equations using a variant of the Hirota bilinearization method. Their results have applications in pulse shaping in nonlinear optics. Calogero et al [32] present examples of systems of ODEs with quadratic nonlinearities that could describe rate equations in chemical dynamics. They derive explicit conditions on the parameters of the problem for which the solutions are periodic and isochronous. Ablowitz and Haut [33] study the motion of large amplitude water waves with surface tension using asymptotic expansions and providing a comparison with experimental results. This issue is the result of the collaboration of many individuals. We would like to thank the editors and staff of the Journal of Physics A: Mathematical and Theoretical for their enthusiastic support and efficient help during the preparation of this issue. A key factor has been the work of many anonymous referees who performed careful analysis and scrutiny of the research papers submitted to this issue, often making remarks which helped to improve their quality and readability. They carried out dedicated, altruistic work with a very high standard and this issue would not exist without their contribution. Finally, we would like to thank the authors who responded to our open call, sending us their most recent results and sharing with us the enthusiasm and interest for this fascinating field of research. We hope that this collection of papers will provide a good overview for anyone interested in recent developments in the field of integrability and nonlinear phenomena. [1] Integrable models in nonlinear optics and soliton solutions Degasperis A [2] Hamiltonian PDEs: deformations, integrability, solutions Dubrovin B [3] Smooth and peaked solitons of the CH equation Holm D D and Ivanov R I [4] KP solitons in shallow water Kodama Y [5] Two extensions of 1D Toda hierarchy Takasaki K [6] On the Lax representation of the 2-component KP and 2D Toda hierarchies Guido Carlet and Manuel Manas [7] The q-deformed mKP hierarchy with self-consistent sources, Wronskian solutions and solitons Lin R L, Peng H and Manas M [8] Hodograph solutions of the dispersionless coupled KdV hierarchies, critical points and the Euler-Poisson-Darboux equation Konopelchenko B, Martinez Alonso L and E Medina [9] Non-Hamiltonian generalizations of the dispersionless 2DTL hierarchy Bogdanov L V [10] Squared eigenfunctions and the perturbation theory for the nondegenerate N x N operator: a general outline Kaup D J and Van Gorder R A [11] The noncommutative AKNS system: projection to matrix systems, countable superposition and soliton-like solutions Schiebold C [12] On the soliton solutions of the two-dimensional Toda lattice Biondini G and Wang D [13] Differential algebra of the Painleve property Benes G N and Previato E [14] Klein's curve Braden H W and Northover T P [15] Quantum monodromy and pattern formation Zhilinskii B [16] A symptotics for a special solution to the second member of the Painleve I hierarchy Claeys T [17] Darboux transformation for a two-component derivative nonlinear Schroedinger equation Ling L and Liu Q P [18] Backlund transformations as exact integrable time discretizations for the trigonometric Gaudin model Ragnisco O and Zullo F [19] Exceptional orthogonal polynomials and the Darboux transformation Gomez-Ullate D, Kamran N and Milson R [20] The hydrodynamic Chaplygin sleigh Fedorov Y N and Garcia-Naranjo L C [21] A normal form for beam and non-local nonlinear Schroedinger equations Procesi M [22] Nonlocal transformations and linearization of second-order ordinary differential equations Muriel and Romero J L [23] Reductions of integrable equations on A.III-type symmetric spaces Gerdjikov V S, Mikhailov A V and Valchev T I [24] On Darboux-integrable semi-discrete chains Habibullin I, Zheltukhina N and Sakieva A [25] Loop coproducts, Gaudin models and Poisson coalgebras Musso F [26] Classification of integrable hydrodynamic chains Odesskii A V and Sokolov V V [27] Noncommutative Schur polynomials and the crystal limit of the Uq sl(2)-vertex model Korff C [28] Axially symmetric soliton solutions in a Skyrme-Faddeev-type model with Gies's extension Ferreira L A, Sawado N and Toda K [29] Vortices on hyperbolic surfaces Manton N S and Rink N A [30] Multivariate hypergeometric cascades, isomonodromy problems and Ward ansatze Shah M R and Woodhouse N J M [31] Coherently coupled bright optical solitons and their collisions Kanna T, Vijayajayanthi M and Lakshmanan M [32] Isochronous rate equations describing chemical reactions Calogero F, Leyvraz F and Sommacal M [33] Asymptotic expansions for solitary gravity-capillary waves in two and three dimensions Ablowitz M J and Haut T S

Analysis of crack propagation in roller bearings using the boundary integral equation method - A mixed-mode loading problem

NASA Technical Reports Server (NTRS)

Ghosn, L. J.

1988-01-01

Crack propagation in a rotating inner raceway of a high-speed roller bearing is analyzed using the boundary integral method. The model consists of an edge plate under plane strain condition upon which varying Hertzian stress fields are superimposed. A multidomain boundary integral equation using quadratic elements was written to determine the stress intensity factors KI and KII at the crack tip for various roller positions. The multidomain formulation allows the two faces of the crack to be modeled in two different subregions, making it possible to analyze crack closure when the roller is positioned on or close to the crack line. KI and KII stress intensity factors along any direction were computed. These calculations permit determination of crack growth direction along which the average KI times the alternating KI is maximum.

Towards a theory of cortical columns: From spiking neurons to interacting neural populations of finite size.

PubMed

Schwalger, Tilo; Deger, Moritz; Gerstner, Wulfram

2017-04-01

Neural population equations such as neural mass or field models are widely used to study brain activity on a large scale. However, the relation of these models to the properties of single neurons is unclear. Here we derive an equation for several interacting populations at the mesoscopic scale starting from a microscopic model of randomly connected generalized integrate-and-fire neuron models. Each population consists of 50-2000 neurons of the same type but different populations account for different neuron types. The stochastic population equations that we find reveal how spike-history effects in single-neuron dynamics such as refractoriness and adaptation interact with finite-size fluctuations on the population level. Efficient integration of the stochastic mesoscopic equations reproduces the statistical behavior of the population activities obtained from microscopic simulations of a full spiking neural network model. The theory describes nonlinear emergent dynamics such as finite-size-induced stochastic transitions in multistable networks and synchronization in balanced networks of excitatory and inhibitory neurons. The mesoscopic equations are employed to rapidly integrate a model of a cortical microcircuit consisting of eight neuron types, which allows us to predict spontaneous population activities as well as evoked responses to thalamic input. Our theory establishes a general framework for modeling finite-size neural population dynamics based on single cell and synapse parameters and offers an efficient approach to analyzing cortical circuits and computations.

Stability Results, Almost Global Generalized Beltrami Fields and Applications to Vortex Structures in the Euler Equations

NASA Astrophysics Data System (ADS)

Enciso, Alberto; Poyato, David; Soler, Juan

2018-05-01

Strong Beltrami fields, that is, vector fields in three dimensions whose curl is the product of the field itself by a constant factor, have long played a key role in fluid mechanics and magnetohydrodynamics. In particular, they are the kind of stationary solutions of the Euler equations where one has been able to show the existence of vortex structures (vortex tubes and vortex lines) of arbitrarily complicated topology. On the contrary, there are very few results about the existence of generalized Beltrami fields, that is, divergence-free fields whose curl is the field times a non-constant function. In fact, generalized Beltrami fields (which are also stationary solutions to the Euler equations) have been recently shown to be rare, in the sense that for "most" proportionality factors there are no nontrivial Beltrami fields of high enough regularity (e.g., of class {C^{6,α}}), not even locally. Our objective in this work is to show that, nevertheless, there are "many" Beltrami fields with non-constant factor, even realizing arbitrarily complicated vortex structures. This fact is relevant in the study of turbulent configurations. The core results are an "almost global" stability theorem for strong Beltrami fields, which ensures that a global strong Beltrami field with suitable decay at infinity can be perturbed to get "many" Beltrami fields with non-constant factor of arbitrarily high regularity and defined in the exterior of an arbitrarily small ball, and a "local" stability theorem for generalized Beltrami fields, which is an analogous perturbative result which is valid for any kind of Beltrami field (not just with a constant factor) but only applies to small enough domains. The proof relies on an iterative scheme of Grad-Rubin type. For this purpose, we study the Neumann problem for the inhomogeneous Beltrami equation in exterior domains via a boundary integral equation method and we obtain Hölder estimates, a sharp decay at infinity and some compactness properties for these sequences of approximate solutions. Some of the parts of the proof are of independent interest.

A self-consistent two-fluid model of a magnetized plasma-wall transition

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gyergyek, T.; Jožef Stefan Institute, Jamova 39, P.O. Box 100, 1000 Ljubljana; Kovačič, J.

A self-consistent one-dimensional two-fluid model of the magnetized plasma-wall transition is presented. The model includes magnetic field, elastic collisions between ions and electrons, and creation/annihilation of charged particles. Two systems of differential equations are derived. The first system describes the whole magnetized plasma-wall transition region, which consists of the pre-sheath, the magnetized pre-sheath (Chodura layer), and the sheath, which is not neutral, but contains a positive space charge. The second system of equations describes only the neutral part of the plasma-wall transition region—this means only the pre-sheath and the Chodura layer, but not also the sheath. Both systems are solvedmore » numerically. The first system of equations has two singularities. The first occurs when ion velocity in the direction perpendicularly to the wall drops below the ion thermal velocity. The second occurs when the electron velocity in the direction perpendicularly to the wall exceeds the electron thermal velocity. The second system of differential equations only has one singularity, which has also been derived analytically. For finite electron to ion mass ratio, the integration of the second system always breaks down before the Bohm criterion is fulfilled. Some properties of the first system of equations are examined. It is shown that the increased collision frequency demagnetizes the plasma. On the other hand, if the magnetic field is so strong that the ion Larmor radius and the Debye length are comparable, the electron velocity in the direction perpendicularly to the wall reaches the electron thermal velocity before the ion velocity in the direction perpendicularly to the wall reaches the ion sound velocity. In this case, the integration of the model equations breaks down before the Bohm criterion is fulfilled and the sheath is formed.« less

An analytical theory of radio-wave scattering from meteoric ionization - I. Basic equation

NASA Astrophysics Data System (ADS)

Pecina, P.

2016-01-01

We have developed an analytical theory of radio-wave scattering from ionization of meteoric origin. It is based on an integro-differential equation for the polarization vector, P, inside the meteor trail, representing an analytical solution of the set of Maxwell equations, in combination with a generalized radar equation involving an integral of the trail volume electron density, Ne, and P represented by an auxiliary vector, Q, taken over the whole trail volume. During the derivation of the final formulae, the following assumptions were applied: transversal as well as longitudinal dimensions of the meteor trail are small compared with the distances of the relevant trail point to both the transmitter and receiver and the ratio of these distances to the wavelength of the wave emitted by the radar is very large, so that the stationary-phase method can be employed for evaluation of the relevant integrals. Further, it is shown that in the case of sufficiently low electron density, Ne, corresponding to the case of underdense trails, the classical McKinley's radar equation results as a special case of the general theory. The same also applies regarding the Fresnel characteristics. Our approach is also capable of yielding solutions to the problems of the formation of Fresnel characteristics on trails having any electron density, forward scattering and scattering on trails immersed in the magnetic field. However, we have also shown that the geomagnetic field can be removed from consideration, due to its low strength. The full solution of the above integro-differential equation, valid for any electron volume densities, has been left to subsequent works dealing with this particular problem, due to its complexity.

Viriato: a Fourier-Hermite spectral code for strongly magnetised fluid-kinetic plasma dynamics

NASA Astrophysics Data System (ADS)

Loureiro, Nuno; Dorland, William; Fazendeiro, Luis; Kanekar, Anjor; Mallet, Alfred; Zocco, Alessandro

2015-11-01

We report on the algorithms and numerical methods used in Viriato, a novel fluid-kinetic code that solves two distinct sets of equations: (i) the Kinetic Reduced Electron Heating Model equations [Zocco & Schekochihin, 2011] and (ii) the kinetic reduced MHD (KRMHD) equations [Schekochihin et al., 2009]. Two main applications of these equations are magnetised (Alfvnénic) plasma turbulence and magnetic reconnection. Viriato uses operator splitting to separate the dynamics parallel and perpendicular to the ambient magnetic field (assumed strong). Along the magnetic field, Viriato allows for either a second-order accurate MacCormack method or, for higher accuracy, a spectral-like scheme. Perpendicular to the field Viriato is pseudo-spectral, and the time integration is performed by means of an iterative predictor-corrector scheme. In addition, a distinctive feature of Viriato is its spectral representation of the parallel velocity-space dependence, achieved by means of a Hermite representation of the perturbed distribution function. A series of linear and nonlinear benchmarks and tests are presented, with focus on 3D decaying kinetic turbulence. Work partially supported by Fundação para a Ciência e Tecnologia via Grants UID/FIS/50010/2013 and IF/00530/2013.

Iterative Methods to Solve Linear RF Fields in Hot Plasma

NASA Astrophysics Data System (ADS)

Spencer, Joseph; Svidzinski, Vladimir; Evstatiev, Evstati; Galkin, Sergei; Kim, Jin-Soo

2014-10-01

Most magnetic plasma confinement devices use radio frequency (RF) waves for current drive and/or heating. Numerical modeling of RF fields is an important part of performance analysis of such devices and a predictive tool aiding design and development of future devices. Prior attempts at this modeling have mostly used direct solvers to solve the formulated linear equations. Full wave modeling of RF fields in hot plasma with 3D nonuniformities is mostly prohibited, with memory demands of a direct solver placing a significant limitation on spatial resolution. Iterative methods can significantly increase spatial resolution. We explore the feasibility of using iterative methods in 3D full wave modeling. The linear wave equation is formulated using two approaches: for cold plasmas the local cold plasma dielectric tensor is used (resolving resonances by particle collisions), while for hot plasmas the conductivity kernel (which includes a nonlocal dielectric response) is calculated by integrating along test particle orbits. The wave equation is discretized using a finite difference approach. The initial guess is important in iterative methods, and we examine different initial guesses including the solution to the cold plasma wave equation. Work is supported by the U.S. DOE SBIR program.

Investigation of Volumetric Sources in Airframe Noise Simulations

NASA Technical Reports Server (NTRS)

Casper, Jay H.; Lockard, David P.; Khorrami, Mehdi R.; Streett, Craig L.

2004-01-01

Hybrid methods for the prediction of airframe noise involve a simulation of the near field flow that is used as input to an acoustic propagation formula. The acoustic formulations discussed herein are those based on the Ffowcs Williams and Hawkings equation. Some questions have arisen in the published literature in regard to an apparently significant dependence of radiated noise predictions on the location of the integration surface used in the solution of the Ffowcs Williams and Hawkings equation. These differences in radiated noise levels are most pronounced between solid-body surface integrals and off-body, permeable surface integrals. Such differences suggest that either a non-negligible volumetric source is contributing to the total radiation or the input flow simulation is suspect. The focus of the current work is the issue of internal consistency of the flow calculations that are currently used as input to airframe noise predictions. The case study for this research is a computer simulation for a three-element, high-lift wing profile during landing conditions. The noise radiated from this flow is predicted by a two-dimensional, frequency-domain formulation of the Ffowcs Williams and Hawkings equation. Radiated sound from volumetric sources is assessed by comparison of a permeable surface integration with the sum of a solid-body surface integral and a volume integral. The separate noise predictions are found in good agreement.

Constant fields and constant gradients in open ionic channels.

PubMed Central

Chen, D P; Barcilon, V; Eisenberg, R S

1992-01-01

Ions enter cells through pores in proteins that are holes in dielectrics. The energy of interaction between ion and charge induced on the dielectric is many kT, and so the dielectric properties of channel and pore are important. We describe ionic movement by (three-dimensional) Nemst-Planck equations (including flux and net charge). Potential is described by Poisson's equation in the pore and Laplace's equation in the channel wall, allowing induced but not permanent charge. Asymptotic expansions are constructed exploiting the long narrow shape of the pore and the relatively high dielectric constant of the pore's contents. The resulting one-dimensional equations can be integrated numerically; they can be analyzed when channels are short or long (compared with the Debye length). Traditional constant field equations are derived if the induced charge is small, e.g., if the channel is short or if the total concentration gradient is zero. A constant gradient of concentration is derived if the channel is long. Plots directly comparable to experiments are given of current vs voltage, reversal potential vs. concentration, and slope conductance vs. concentration. This dielectric theory can easily be tested: its parameters can be determined by traditional constant field measurements. The dielectric theory then predicts current-voltage relations quite different from constant field, usually more linear, when gradients of total concentration are imposed. Numerical analysis shows that the interaction of ion and channel can be described by a mean potential if, but only if, the induced charge is negligible, that is to say, the electric field is spatially constant. Images FIGURE 1 PMID:1376159

Analytic integration of real-virtual counterterms in NNLO jet cross sections I

NASA Astrophysics Data System (ADS)

Aglietti, Ugo; Del Duca, Vittorio; Duhr, Claude; Somogyi, Gábor; Trócsányi, Zoltán

2008-09-01

We present analytic evaluations of some integrals needed to give explicitly the integrated real-virtual counterterms, based on a recently proposed subtraction scheme for next-to-next-to-leading order (NNLO) jet cross sections. After an algebraic reduction of the integrals, integration-by-parts identities are used for the reduction to master integrals and for the computation of the master integrals themselves by means of differential equations. The results are written in terms of one- and two-dimensional harmonic polylogarithms, once an extension of the standard basis is made. We expect that the techniques described here will be useful in computing other integrals emerging in calculations in perturbative quantum field theories.

Application of a Near-Field Water Quality Model.

DTIC Science & Technology

1979-07-01

VERIFICATION 45 CENTERLINE TEMPERATURE DECRF~A7F 46 LATERAL VARIATION OF CONSTITUENTS 46 VARIATIOtN OF PLUME WIDTH 49 GENERAL ON VERIFICATION 49...40 4 SOME RESULTS OF VARYING THE ENTRAINMENT COEFFICIENT 4’ 5 RESULTS OF VARYING OTHER COEFFICEINT 42 6 GENERAL PLUME CHARACTERISITICS FOR VARIATION... plume ) axis. These profile forms are then integrated within the basic conservation equations. This integration reduces the problem to a one

Integrable systems with BMS3 Poisson structure and the dynamics of locally flat spacetimes

NASA Astrophysics Data System (ADS)

Fuentealba, Oscar; Matulich, Javier; Pérez, Alfredo; Pino, Miguel; Rodríguez, Pablo; Tempo, David; Troncoso, Ricardo

2018-01-01

We construct a hierarchy of integrable systems whose Poisson structure corresponds to the BMS3 algebra, and then discuss its description in terms of the Riemannian geometry of locally flat spacetimes in three dimensions. The analysis is performed in terms of two-dimensional gauge fields for isl(2,R) , being isomorphic to the Poincaré algebra in 3D. Although the algebra is not semisimple, the formulation can still be carried out à la Drinfeld-Sokolov because it admits a nondegenerate invariant bilinear metric. The hierarchy turns out to be bi-Hamiltonian, labeled by a nonnegative integer k, and defined through a suitable generalization of the Gelfand-Dikii polynomials. The symmetries of the hierarchy are explicitly found. For k ≥ 1, the corresponding conserved charges span an infinite-dimensional Abelian algebra without central extensions, so that they are in involution; while in the case of k = 0, they generate the BMS3 algebra. In the special case of k = 1, by virtue of a suitable field redefinition and time scaling, the field equations are shown to be equivalent to the ones of a specific type of the Hirota-Satsuma coupled KdV systems. For k ≥ 1, the hierarchy also includes the so-called perturbed KdV equations as a particular case. A wide class of analytic solutions is also explicitly constructed for a generic value of k. Remarkably, the dynamics can be fully geometrized so as to describe the evolution of spacelike surfaces embedded in locally flat spacetimes. Indeed, General Relativity in 3D can be endowed with a suitable set of boundary conditions, so that the Einstein equations precisely reduce to the ones of the hierarchy aforementioned. The symmetries of the integrable systems then arise as diffeomorphisms that preserve the asymptotic form of the spacetime metric, and therefore, they become Noetherian. The infinite set of conserved charges is then recovered from the corresponding surface integrals in the canonical approach.

Traveling waves in Hall-magnetohydrodynamics and the ion-acoustic shock structure

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hagstrom, George I.; Hameiri, Eliezer

Hall-magnetohydrodynamics (HMHD) is a mixed hyperbolic-parabolic partial differential equation that describes the dynamics of an ideal two fluid plasma with massless electrons. We study the only shock wave family that exists in this system (the other discontinuities being contact discontinuities and not shocks). We study planar traveling wave solutions and we find solutions with discontinuities in the hydrodynamic variables, which arise due to the presence of real characteristics in Hall-MHD. We introduce a small viscosity into the equations and use the method of matched asymptotic expansions to show that solutions with a discontinuity satisfying the Rankine-Hugoniot conditions and also anmore » entropy condition have continuous shock structures. The lowest order inner equations reduce to the compressible Navier-Stokes equations, plus an equation which implies the constancy of the magnetic field inside the shock structure. We are able to show that the current is discontinuous across the shock, even as the magnetic field is continuous, and that the lowest order outer equations, which are the equations for traveling waves in inviscid Hall-MHD, are exactly integrable. We show that the inner and outer solutions match, which allows us to construct a family of uniformly valid continuous composite solutions that become discontinuous when the diffusivity vanishes.« less

Multiple and exact soliton solutions of the perturbed Korteweg-de Vries equation of long surface waves in a convective fluid via Painlevé analysis, factorization, and simplest equation methods.

PubMed

Selima, Ehab S; Yao, Xiaohua; Wazwaz, Abdul-Majid

2017-06-01

In this research, the surface waves of a horizontal fluid layer open to air under gravity field and vertical temperature gradient effects are studied. The governing equations of this model are reformulated and converted to a nonlinear evolution equation, the perturbed Korteweg-de Vries (pKdV) equation. We investigate the latter equation, which includes dispersion, diffusion, and instability effects, in order to examine the evolution of long surface waves in a convective fluid. Dispersion relation of the pKdV equation and its properties are discussed. The Painlevé analysis is applied not only to check the integrability of the pKdV equation but also to establish the Bäcklund transformation form. In addition, traveling wave solutions and a general form of the multiple-soliton solutions of the pKdV equation are obtained via Bäcklund transformation, the simplest equation method using Bernoulli, Riccati, and Burgers' equations as simplest equations, and the factorization method.

Flow Mapping Based on the Motion-Integration Errors of Autonomous Underwater Vehicles

NASA Astrophysics Data System (ADS)

Chang, D.; Edwards, C. R.; Zhang, F.

2016-02-01

Knowledge of a flow field is crucial in the navigation of autonomous underwater vehicles (AUVs) since the motion of AUVs is affected by ambient flow. Due to the imperfect knowledge of the flow field, it is typical to observe a difference between the actual and predicted trajectories of an AUV, which is referred to as a motion-integration error (also known as a dead-reckoning error if an AUV navigates via dead-reckoning). The motion-integration error has been essential for an underwater glider to compute its flow estimate from the travel information of the last leg and to improve navigation performance by using the estimate for the next leg. However, the estimate by nature exhibits a phase difference compared to ambient flow experienced by gliders, prohibiting its application in a flow field with strong temporal and spatial gradients. In our study, to mitigate the phase problem, we have developed a local ocean model by combining the flow estimate based on the motion-integration error with flow predictions from a tidal ocean model. Our model has been used to create desired trajectories of gliders for guidance. Our method is validated by Long Bay experiments in 2012 and 2013 in which we deployed multiple gliders on the shelf of South Atlantic Bight and near the edge of Gulf Stream. In our recent study, the application of the motion-integration error is further extended to create a spatial flow map. Considering that the motion-integration errors of AUVs accumulate along their trajectories, the motion-integration error is formulated as a line integral of ambient flow which is then reformulated into algebraic equations. By solving an inverse problem for these algebraic equations, we obtain the knowledge of such flow in near real time, allowing more effective and precise guidance of AUVs in a dynamic environment. This method is referred to as motion tomography. We provide the results of non-parametric and parametric flow mapping from both simulated and experimental data.

A numerical relativity scheme for cosmological simulations

NASA Astrophysics Data System (ADS)

Daverio, David; Dirian, Yves; Mitsou, Ermis

2017-12-01

Cosmological simulations involving the fully covariant gravitational dynamics may prove relevant in understanding relativistic/non-linear features and, therefore, in taking better advantage of the upcoming large scale structure survey data. We propose a new 3  +  1 integration scheme for general relativity in the case where the matter sector contains a minimally-coupled perfect fluid field. The original feature is that we completely eliminate the fluid components through the constraint equations, thus remaining with a set of unconstrained evolution equations for the rest of the fields. This procedure does not constrain the lapse function and shift vector, so it holds in arbitrary gauge and also works for arbitrary equation of state. An important advantage of this scheme is that it allows one to define and pass an adaptation of the robustness test to the cosmological context, at least in the case of pressureless perfect fluid matter, which is the relevant one for late-time cosmology.

Homogeneous quantum electrodynamic turbulence

NASA Technical Reports Server (NTRS)

Shebalin, John V.

1992-01-01

The electromagnetic field equations and Dirac equations for oppositely charged wave functions are numerically time-integrated using a spatial Fourier method. The numerical approach used, a spectral transform technique, is based on a continuum representation of physical space. The coupled classical field equations contain a dimensionless parameter which sets the strength of the nonlinear interaction (as the parameter increases, interaction volume decreases). For a parameter value of unity, highly nonlinear behavior in the time-evolution of an individual wave function, analogous to ideal fluid turbulence, is observed. In the truncated Fourier representation which is numerically implemented here, the quantum turbulence is homogeneous but anisotropic and manifests itself in the nonlinear evolution of equilibrium modal spatial spectra for the probability density of each particle and also for the electromagnetic energy density. The results show that nonlinearly interacting fermionic wave functions quickly approach a multi-mode, dynamic equilibrium state, and that this state can be determined by numerical means.

Theoretical model for thin ferroelectric films and the multilayer structures based on them

NASA Astrophysics Data System (ADS)

Starkov, A. S.; Pakhomov, O. V.; Starkov, I. A.

2013-06-01

A modified Weiss mean-field theory is used to study the dependence of the properties of a thin ferroelectric film on its thickness. The possibility of introducing gradient terms into the thermodynamic potential is analyzed using the calculus of variations. An integral equation is introduced to generalize the well-known Langevin equation to the case of the boundaries of a ferroelectric. An analysis of this equation leads to the existence of a transition layer at the interface between ferroelectrics or a ferroelectric and a dielectric. The permittivity of this layer is shown to depend on the electric field direction even if the ferroelectrics in contact are homogeneous. The results obtained in terms of the Weiss model are compared with the results of the models based on the correlation effect and the presence of a dielectric layer at the boundary of a ferroelectric and with experimental data.

High Energy Laser Beam Propagation in the Atmosphere: The Integral Invariants of the Nonlinear Parabolic Equation and the Method of Moments

NASA Technical Reports Server (NTRS)

Manning, Robert M.

2012-01-01

The method of moments is used to define and derive expressions for laser beam deflection and beam radius broadening for high-energy propagation through the Earth s atmosphere. These expressions are augmented with the integral invariants of the corresponding nonlinear parabolic equation that describes the electric field of high-energy laser beam to propagation to yield universal equations for the aforementioned quantities; the beam deflection is a linear function of the propagation distance whereas the beam broadening is a quadratic function of distance. The coefficients of these expressions are then derived from a thin screen approximation solution of the nonlinear parabolic equation to give corresponding analytical expressions for a target located outside the Earth s atmospheric layer. These equations, which are graphically presented for a host of propagation scenarios, as well as the thin screen model, are easily amenable to the phase expansions of the wave front for the specification and design of adaptive optics algorithms to correct for the inherent phase aberrations. This work finds application in, for example, the analysis of beamed energy propulsion for space-based vehicles.

Generalizations of the classical Yang-Baxter equation and O-operators

NASA Astrophysics Data System (ADS)

Bai, Chengming; Guo, Li; Ni, Xiang

2011-06-01

Tensor solutions (r-matrices) of the classical Yang-Baxter equation (CYBE) in a Lie algebra, obtained as the classical limit of the R-matrix solution of the quantum Yang-Baxter equation, is an important structure appearing in different areas such as integrable systems, symplectic geometry, quantum groups, and quantum field theory. Further study of CYBE led to its interpretation as certain operators, giving rise to the concept of {O}-operators. The O-operators were in turn interpreted as tensor solutions of CYBE by enlarging the Lie algebra [Bai, C., "A unified algebraic approach to the classical Yang-Baxter equation," J. Phys. A: Math. Theor. 40, 11073 (2007)], 10.1088/1751-8113/40/36/007. The purpose of this paper is to extend this study to a more general class of operators that were recently introduced [Bai, C., Guo, L., and Ni, X., "Nonabelian generalized Lax pairs, the classical Yang-Baxter equation and PostLie algebras," Commun. Math. Phys. 297, 553 (2010)], 10.1007/s00220-010-0998-7 in the study of Lax pairs in integrable systems. Relations between O-operators, relative differential operators, and Rota-Baxter operators are also discussed.

A Formalism for Covariant Polarized Radiative Transport by Ray Tracing

NASA Astrophysics Data System (ADS)

Gammie, Charles F.; Leung, Po Kin

2012-06-01

We write down a covariant formalism for polarized radiative transfer appropriate for ray tracing through a turbulent plasma. The polarized radiation field is represented by the polarization tensor (coherency matrix) N αβ ≡ langa α k a*β k rang, where ak is a Fourier coefficient for the vector potential. Using Maxwell's equations, the Liouville-Vlasov equation, and the WKB approximation, we show that the transport equation in vacuo is k μ∇μ N αβ = 0. We show that this is equivalent to Broderick & Blandford's formalism based on invariant Stokes parameters and a rotation coefficient, and suggest a modification that may reduce truncation error in some situations. Finally, we write down several alternative approaches to integrating the transfer equation.

I -Love- Q relations for white dwarf stars

NASA Astrophysics Data System (ADS)

Boshkayev, K.; Quevedo, H.; Zhami, B.

2017-02-01

We investigate the equilibrium configurations of uniformly rotating white dwarfs, using Chandrasekhar and Salpeter equations of state in the framework of Newtonian physics. The Hartle formalism is applied to integrate the field equation together with the hydrostatic equilibrium condition. We consider the equations of structure up to the second order in the angular velocity, and compute all basic parameters of rotating white dwarfs to test the so-called moment of inertia, rotational Love number, and quadrupole moment (I-Love-Q) relations. We found that the I-Love-Q relations are also valid for white dwarfs regardless of the equation of state and nuclear composition. In addition, we show that the moment of inertia, quadrupole moment, and eccentricity (I-Q-e) relations are valid as well.

Scalable Nonlinear Solvers for Fully Implicit Coupled Nuclear Fuel Modeling. Final Report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cai, Xiao-Chuan; Keyes, David; Yang, Chao

2014-09-29

The focus of the project is on the development and customization of some highly scalable domain decomposition based preconditioning techniques for the numerical solution of nonlinear, coupled systems of partial differential equations (PDEs) arising from nuclear fuel simulations. These high-order PDEs represent multiple interacting physical fields (for example, heat conduction, oxygen transport, solid deformation), each is modeled by a certain type of Cahn-Hilliard and/or Allen-Cahn equations. Most existing approaches involve a careful splitting of the fields and the use of field-by-field iterations to obtain a solution of the coupled problem. Such approaches have many advantages such as ease of implementationmore » since only single field solvers are needed, but also exhibit disadvantages. For example, certain nonlinear interactions between the fields may not be fully captured, and for unsteady problems, stable time integration schemes are difficult to design. In addition, when implemented on large scale parallel computers, the sequential nature of the field-by-field iterations substantially reduces the parallel efficiency. To overcome the disadvantages, fully coupled approaches have been investigated in order to obtain full physics simulations.« less

A Numerical Method of Calculating Propeller Noise Including Acoustic Nonlinear Effects

NASA Technical Reports Server (NTRS)

Korkan, K. D.

1985-01-01

Using the transonic flow fields(s) generated by the NASPROP-E computer code for an eight blade SR3-series propeller, a theoretical method is investigated to calculate the total noise values and frequency content in the acoustic near and far field without using the Ffowcs Williams - Hawkings equation. The flow field is numerically generated using an implicit three dimensional Euler equation solver in weak conservation law form. Numerical damping is required by the differencing method for stability in three dimensions, and the influence of the damping on the calculated acoustic values is investigated. The acoustic near field is solved by integrating with respect to time the pressure oscillations induced at a stationary observer location. The acoustic far field is calculated from the near field primitive variables as generated by NASPROP-E computer code using a method involving a perturbation velocity potential as suggested by Hawkings in the calculation of the acoustic pressure time-history at a specified far field observed location. the methodologies described are valid for calculating total noise levels and are applicable to any propeller geometry for which a flow field solution is available.

Collocation for an integral equation arising in duct acoustics

NASA Technical Reports Server (NTRS)

Moss, W. F.

1986-01-01

A mathematical model is developed to describe the effect of aircraft-engine inlet geometry on the reflected and radiated acoustic field without flow, as studied experimentally using a spinning-mode synthesizer by Silcox (1983). The acoustic pressure in the inlet interior and exterior is modeled by a pure cylindrical azimuthal mode for the Helmholtz equation with hardwall boundary and by the Helmholtz equation and the radiation condition at infinity, respectively. The analytical approach to the solution of the resulting boundary-value problem and the program implementation are explained; numerical results are presented in tables and graphs; and the uniqueness of the problem is demonstrated.

Time-Domain Computation Of Electromagnetic Fields In MMICs

NASA Technical Reports Server (NTRS)

Lansing, Faiza S.; Rascoe, Daniel L.

1995-01-01

Maxwell's equations solved on three-dimensional, conformed orthogonal grids by finite-difference techniques. Method of computing frequency-dependent electrical parameters of monolithic microwave integrated circuit (MMIC) involves time-domain computation of propagation of electromagnetic field in response to excitation by single pulse at input terminal, followed by computation of Fourier transforms to obtain frequency-domain response from time-domain response. Parameters computed include electric and magnetic fields, voltages, currents, impedances, scattering parameters, and effective dielectric constants. Powerful and efficient means for analyzing performance of even complicated MMIC.

Analysis of mixed-mode crack propagation using the boundary integral method

NASA Technical Reports Server (NTRS)

Mendelson, A.; Ghosn, L. J.

1986-01-01

Crack propagation in a rotating inner raceway of a high speed roller bearing is analyzed using the boundary integral equation method. The method consists of an edge crack in a plate under tension, upon which varying Hertzian stress fields are superimposed. A computer program for the boundary integral equation method was written using quadratic elements to determine the stress and displacement fields for discrete roller positions. Mode I and Mode II stress intensity factors and crack extension forces G sub 00 (energy release rate due to tensile opening mode) and G sub r0 (energy release rate due to shear displacement mode) were computed. These calculations permit determination of that crack growth angle for which the change in the crack extension forces is maximum. The crack driving force was found to be the alternating mixed-mode loading that occurs with each passage of the most heavily loaded roller. The crack is predicted to propagate in a step-like fashion alternating between radial and inclined segments, and this pattern was observed experimentally. The maximum changes DeltaG sub 00 and DeltaG sub r0 of the crack extension forces are found to be good measures of the crack propagation rate and direction.

Developing semi-analytical solution for multiple-zone transient storage model with spatially non-uniform storage

NASA Astrophysics Data System (ADS)

Deng, Baoqing; Si, Yinbing; Wang, Jia

2017-12-01

Transient storages may vary along the stream due to stream hydraulic conditions and the characteristics of storage. Analytical solutions of transient storage models in literature didn't cover the spatially non-uniform storage. A novel integral transform strategy is presented that simultaneously performs integral transforms to the concentrations in the stream and in storage zones by using the single set of eigenfunctions derived from the advection-diffusion equation of the stream. The semi-analytical solution of the multiple-zone transient storage model with the spatially non-uniform storage is obtained by applying the generalized integral transform technique to all partial differential equations in the multiple-zone transient storage model. The derived semi-analytical solution is validated against the field data in literature. Good agreement between the computed data and the field data is obtained. Some illustrative examples are formulated to demonstrate the applications of the present solution. It is shown that solute transport can be greatly affected by the variation of mass exchange coefficient and the ratio of cross-sectional areas. When the ratio of cross-sectional areas is big or the mass exchange coefficient is small, more reaches are recommended to calibrate the parameter.

Optical fringe-reflection deflectometry with sparse representation

NASA Astrophysics Data System (ADS)

Xiao, Yong-Liang; Li, Sikun; Zhang, Qican; Zhong, Jianxin; Su, Xianyu; You, Zhisheng

2018-05-01

Optical fringe-reflection deflectometry is a surprisingly attractive scratch detection technique for specular surfaces owing to its unparalleled local sensibility. Full-field surface topography is obtained from a measured normal field using gradient integration. However, there may not be an ideal measured gradient field for deflectometry reconstruction in practice. Both the non-integrability condition and various kinds of image noise distributions, which are present in the indirect measured gradient field, may lead to ambiguity about the scratches on specular surfaces. In order to reduce misjudgment of scratches, sparse representation is introduced into the Southwell curl equation for deflectometry. The curl can be represented as a linear combination of the given redundant dictionary for curl and the sparsest solution for gradient refinement. The non-integrability condition and noise permutation can be overcome with sparse representation for gradient refinement. Numerical simulations demonstrate that the accuracy rate of judgment of scratches can be enhanced with sparse representation compared to the standard least-squares integration. Preliminary experiments are performed with the application of practical measured deflectometric data to verify the validity of the algorithm.

General methods for determining the linear stability of coronal magnetic fields

NASA Technical Reports Server (NTRS)

Craig, I. J. D.; Sneyd, A. D.; Mcclymont, A. N.

1988-01-01

A time integration of a linearized plasma equation of motion has been performed to calculate the ideal linear stability of arbitrary three-dimensional magnetic fields. The convergence rates of the explicit and implicit power methods employed are speeded up by using sequences of cyclic shifts. Growth rates are obtained for Gold-Hoyle force-free equilibria, and the corkscrew-kink instability is found to be very weak.

General methods for determining the linear stability of coronal magnetic fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Craig, I.J.D.; Sneyd, A.D.; McClymont, A.N.

1988-12-01

A time integration of a linearized plasma equation of motion has been performed to calculate the ideal linear stability of arbitrary three-dimensional magnetic fields. The convergence rates of the explicit and implicit power methods employed are speeded up by using sequences of cyclic shifts. Growth rates are obtained for Gold-Hoyle force-free equilibria, and the corkscrew-kink instability is found to be very weak. 19 references.

Integral Equation Method for Electromagnetic Wave Propagation in Stratified Anisotropic Dielectric-Magnetic Materials

NASA Astrophysics Data System (ADS)

Shu, Wei-Xing; Fu, Na; Lü, Xiao-Fang; Luo, Hai-Lu; Wen, Shuang-Chun; Fan, Dian-Yuan

2010-11-01

We investigate the propagation of electromagnetic waves in stratified anisotropic dielectric-magnetic materials using the integral equation method (IEM). Based on the superposition principle, we use Hertz vector formulations of radiated fields to study the interaction of wave with matter. We derive in a new way the dispersion relation, Snell's law and reflection/transmission coefficients by self-consistent analyses. Moreover, we find two new forms of the generalized extinction theorem. Applying the IEM, we investigate the wave propagation through a slab and disclose the underlying physics, which are further verified by numerical simulations. The results lead to a unified framework of the IEM for the propagation of wave incident either from a medium or vacuum in stratified dielectric-magnetic materials.

Performance analysis of three dimensional integral equation computations on a massively parallel computer. M.S. Thesis

NASA Technical Reports Server (NTRS)

Logan, Terry G.

1994-01-01

The purpose of this study is to investigate the performance of the integral equation computations using numerical source field-panel method in a massively parallel processing (MPP) environment. A comparative study of computational performance of the MPP CM-5 computer and conventional Cray-YMP supercomputer for a three-dimensional flow problem is made. A serial FORTRAN code is converted into a parallel CM-FORTRAN code. Some performance results are obtained on CM-5 with 32, 62, 128 nodes along with those on Cray-YMP with a single processor. The comparison of the performance indicates that the parallel CM-FORTRAN code near or out-performs the equivalent serial FORTRAN code for some cases.

A General Theory of Unsteady Compressible Potential Aerodynamics

NASA Technical Reports Server (NTRS)

Morino, L.

1974-01-01

The general theory of potential aerodynamic flow around a lifting body having arbitrary shape and motion is presented. By using the Green function method, an integral representation for the potential is obtained for both supersonic and subsonic flow. Under small perturbation assumption, the potential at any point, P, in the field depends only upon the values of the potential and its normal derivative on the surface, sigma, of the body. Hence, if the point P approaches the surface of the body, the representation reduces to an integro-differential equation relating the potential and its normal derivative (which is known from the boundary conditions) on the surface sigma. For the important practical case of small harmonic oscillation around a rest position, the equation reduces to a two-dimensional Fredholm integral equation of second-type. It is shown that this equation reduces properly to the lifting surface theories as well as other classical mathematical formulas. The question of uniqueness is examined and it is shown that, for thin wings, the operator becomes singular as the thickness approaches zero. This fact may yield numerical problems for very thin wings.

Versatile rogue waves in scalar, vector, and multidimensional nonlinear systems

NASA Astrophysics Data System (ADS)

Chen, Shihua; Baronio, Fabio; Soto-Crespo, Jose M.; Grelu, Philippe; Mihalache, Dumitru

2017-11-01

This review is dedicated to recent progress in the active field of rogue waves, with an emphasis on the analytical prediction of versatile rogue wave structures in scalar, vector, and multidimensional integrable nonlinear systems. We first give a brief outline of the historical background of the rogue wave research, including referring to relevant up-to-date experimental results. Then we present an in-depth discussion of the scalar rogue waves within two different integrable frameworks—the infinite nonlinear Schrödinger (NLS) hierarchy and the general cubic-quintic NLS equation, considering both the self-focusing and self-defocusing Kerr nonlinearities. We highlight the concept of chirped Peregrine solitons, the baseband modulation instability as an origin of rogue waves, and the relation between integrable turbulence and rogue waves, each with illuminating examples confirmed by numerical simulations. Later, we recur to the vector rogue waves in diverse coupled multicomponent systems such as the long-wave short-wave equations, the three-wave resonant interaction equations, and the vector NLS equations (alias Manakov system). In addition to their intriguing bright-dark dynamics, a series of other peculiar structures, such as coexisting rogue waves, watch-hand-like rogue waves, complementary rogue waves, and vector dark three sisters, are reviewed. Finally, for practical considerations, we also remark on higher-dimensional rogue waves occurring in three closely-related (2  +  1)D nonlinear systems, namely, the Davey-Stewartson equation, the composite (2  +  1)D NLS equation, and the Kadomtsev-Petviashvili I equation. As an interesting contrast to the peculiar X-shaped light bullets, a concept of rogue wave bullets intended for high-dimensional systems is particularly put forward by combining contexts in nonlinear optics.

A Generalized Eulerian-Lagrangian Analysis, with Application to Liquid Flows with Vapor Bubbles

NASA Technical Reports Server (NTRS)

Dejong, Frederik J.; Meyyappan, Meyya

1993-01-01

Under a NASA MSFC SBIR Phase 2 effort an analysis has been developed for liquid flows with vapor bubbles such as those in liquid rocket engine components. The analysis is based on a combined Eulerian-Lagrangian technique, in which Eulerian conservation equations are solved for the liquid phase, while Lagrangian equations of motion are integrated in computational coordinates for the vapor phase. The novel aspect of the Lagrangian analysis developed under this effort is that it combines features of the so-called particle distribution approach with those of the so-called particle trajectory approach and can, in fact, be considered as a generalization of both of those traditional methods. The result of this generalization is a reduction in CPU time and memory requirements. Particle time step (stability) limitations have been eliminated by semi-implicit integration of the particle equations of motion (and, for certain applications, the particle temperature equation), although practical limitations remain in effect for reasons of accuracy. The analysis has been applied to the simulation of cavitating flow through a single-bladed section of a labyrinth seal. Models for the simulation of bubble formation and growth have been included, as well as models for bubble drag and heat transfer. The results indicate that bubble formation is more or less 'explosive'. for a given flow field, the number density of bubble nucleation sites is very sensitive to the vapor properties and the surface tension. The bubble motion, on the other hand, is much less sensitive to the properties, but is affected strongly by the local pressure gradients in the flow field. In situations where either the material properties or the flow field are not known with sufficient accuracy, parametric studies can be carried out rapidly to assess the effect of the important variables. Future work will include application of the analysis to cavitation in inducer flow fields.

Numerical investigation of turbulent channel flow

NASA Technical Reports Server (NTRS)

Moin, P.; Kim, J.

1981-01-01

Fully developed turbulent channel flow was simulated numerically at Reynolds number 13800, based on centerline velocity and channel halt width. The large-scale flow field was obtained by directly integrating the filtered, three dimensional, time dependent, Navier-Stokes equations. The small-scale field motions were simulated through an eddy viscosity model. The calculations were carried out on the ILLIAC IV computer with up to 516,096 grid points. The computed flow field was used to study the statistical properties of the flow as well as its time dependent features. The agreement of the computed mean velocity profile, turbulence statistics, and detailed flow structures with experimental data is good. The resolvable portion of the statistical correlations appearing in the Reynolds stress equations are calculated. Particular attention is given to the examination of the flow structure in the vicinity of the wall.

Determination of the Geometric Form of a Plane of a Tectonic Gap as the Inverse III-posed Problem of Mathematical Physics

NASA Astrophysics Data System (ADS)

Sirota, Dmitry; Ivanov, Vadim

2017-11-01

Any mining operations influence stability of natural and technogenic massifs are the reason of emergence of the sources of differences of mechanical tension. These sources generate a quasistationary electric field with a Newtonian potential. The paper reviews the method of determining the shape and size of a flat source field with this kind of potential. This common problem meets in many fields of mining: geological exploration mineral resources, ore deposits, control of mining by underground method, determining coal self-heating source, localization of the rock crack's sources and other applied problems of practical physics. This problems are ill-posed and inverse and solved by converting to Fredholm-Uryson integral equation of the first kind. This equation will be solved by A.N. Tikhonov regularization method.

Electromagnetics. Volume 1, Number 4, October-December 1981.

DTIC Science & Technology

1981-01-01

terms. 1.6 Matrix and Operator Theory Integral equations have been cast in approximate numerical form by the moment method (MoM). In this numerical...introduced the eigenmode expansion method to find more properties of the SEM [3.4]. One defines eigenvalues and eigenmodes for the integral operator (kernel...exterior surface of the system. Mechanisms that play a role in the penetration are (1) diffusion through metal skins , (2) field leakage through

A finite element-boundary integral formulation for scattering by three-dimensional cavity-backed apertures

NASA Technical Reports Server (NTRS)

Jin, Jian-Ming; Volakis, John L.

1990-01-01

A numerical technique is proposed for the electromagnetic characterization of the scattering by a three-dimensional cavity-backed aperture in an infinite ground plane. The technique combines the finite element and boundary integral methods to formulate a system of equations for the solution of the aperture fields and those inside the cavity. Specifically, the finite element method is employed to formulate the fields in the cavity region and the boundary integral approach is used in conjunction with the equivalence principle to represent the fields above the ground plane. Unlike traditional approaches, the proposed technique does not require knowledge of the cavity's Green's function and is, therefore, applicable to arbitrary shape depressions and material fillings. Furthermore, the proposed formulation leads to a system having a partly full and partly sparse as well as symmetric and banded matrix which can be solved efficiently using special algorithms.

Global Aspects of Charged Particle Motion in Axially Symmetric Multipole Magnetic Fields

NASA Technical Reports Server (NTRS)

Shebalin, John V.

2003-01-01

The motion of a single charged particle in the space outside of a compact region of steady currents is investigated. The charged particle is assumed to produce negligible electromagnetic radiation, so that its energy is conserved. The source of the magnetic field is represented as a point multipole. After a general description, attention is focused on magnetic fields with axial symmetry. Lagrangian dynamical theory is utilized to identify constants of the motion as well as the equations of motion themselves. The qualitative method of Stonner is used to examine charged particle motion in axisymmetric multipole fields of all orders. Although the equations of motion generally have no analytical solutions and must be integrated numerically to produce a specific orbit, a topological examination of dynamics is possible, and can be used, d la Stonner, to completely describe the global aspects of the motion of a single charged particle in a space with an axisymmetric multipole magnetic field.

A boundary condition to the Khokhlov-Zabolotskaya equation for modeling strongly focused nonlinear ultrasound fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rosnitskiy, P., E-mail: pavrosni@yandex.ru; Yuldashev, P., E-mail: petr@acs366.phys.msu.ru; Khokhlova, V., E-mail: vera@acs366.phys.msu.ru

2015-10-28

An equivalent source model was proposed as a boundary condition to the nonlinear parabolic Khokhlov-Zabolotskaya (KZ) equation to simulate high intensity focused ultrasound (HIFU) fields generated by medical ultrasound transducers with the shape of a spherical shell. The boundary condition was set in the initial plane; the aperture, the focal distance, and the initial pressure of the source were chosen based on the best match of the axial pressure amplitude and phase distributions in the Rayleigh integral analytic solution for a spherical transducer and the linear parabolic approximation solution for the equivalent source. Analytic expressions for the equivalent source parametersmore » were derived. It was shown that the proposed approach allowed us to transfer the boundary condition from the spherical surface to the plane and to achieve a very good match between the linear field solutions of the parabolic and full diffraction models even for highly focused sources with F-number less than unity. The proposed method can be further used to expand the capabilities of the KZ nonlinear parabolic equation for efficient modeling of HIFU fields generated by strongly focused sources.« less

Low-derivative operators of the Standard Model effective field theory via Hilbert series methods

NASA Astrophysics Data System (ADS)

Lehman, Landon; Martin, Adam

2016-02-01

In this work, we explore an extension of Hilbert series techniques to count operators that include derivatives. For sufficiently low-derivative operators, we conjecture an algorithm that gives the number of invariant operators, properly accounting for redundancies due to the equations of motion and integration by parts. Specifically, the conjectured technique can be applied whenever there is only one Lorentz invariant for a given partitioning of derivatives among the fields. At higher numbers of derivatives, equation of motion redundancies can be removed, but the increased number of Lorentz contractions spoils the subtraction of integration by parts redundancies. While restricted, this technique is sufficient to automatically recreate the complete set of invariant operators of the Standard Model effective field theory for dimensions 6 and 7 (for arbitrary numbers of flavors). At dimension 8, the algorithm does not automatically generate the complete operator set; however, it suffices for all but five classes of operators. For these remaining classes, there is a well defined procedure to manually determine the number of invariants. Assuming our method is correct, we derive a set of 535 dimension-8 N f = 1 operators.

A fully implicit numerical integration of the relativistic particle equation of motion

NASA Astrophysics Data System (ADS)

Pétri, J.

2017-04-01

Relativistic strongly magnetized plasmas are produced in laboratories thanks to state-of-the-art laser technology but can naturally be found around compact objects such as neutron stars and black holes. Detailed studies of the behaviour of relativistic plasmas require accurate computations able to catch the full spatial and temporal dynamics of the system. Numerical simulations of ultra-relativistic plasmas face severe restrictions due to limitations in the maximum possible Lorentz factors that current algorithms can reproduce to good accuracy. In order to circumvent this flaw and repel the limit to 9$ , we design a new fully implicit scheme to solve the relativistic particle equation of motion in an external electromagnetic field using a three-dimensional Cartesian geometry. We show some examples of numerical integrations in constant electromagnetic fields to prove the efficiency of our algorithm. The code is also able to follow the electric drift motion for high Lorentz factors. In the most general case of spatially and temporally varying electromagnetic fields, the code performs extremely well, as shown by comparison with exact analytical solutions for the relativistic electrostatic Kepler problem as well as for linearly and circularly polarized plane waves.

An efficient algorithm for the generalized Foldy-Lax formulation

NASA Astrophysics Data System (ADS)

Huang, Kai; Li, Peijun; Zhao, Hongkai

2013-02-01

Consider the scattering of a time-harmonic plane wave incident on a two-scale heterogeneous medium, which consists of scatterers that are much smaller than the wavelength and extended scatterers that are comparable to the wavelength. In this work we treat those small scatterers as isotropic point scatterers and use a generalized Foldy-Lax formulation to model wave propagation and capture multiple scattering among point scatterers and extended scatterers. Our formulation is given as a coupled system, which combines the original Foldy-Lax formulation for the point scatterers and the regular boundary integral equation for the extended obstacle scatterers. The existence and uniqueness of the solution for the formulation is established in terms of physical parameters such as the scattering coefficient and the separation distances. Computationally, an efficient physically motivated Gauss-Seidel iterative method is proposed to solve the coupled system, where only a linear system of algebraic equations for point scatterers or a boundary integral equation for a single extended obstacle scatterer is required to solve at each step of iteration. The convergence of the iterative method is also characterized in terms of physical parameters. Numerical tests for the far-field patterns of scattered fields arising from uniformly or randomly distributed point scatterers and single or multiple extended obstacle scatterers are presented.

PREFACE: Physics and Mathematics of Nonlinear Phenomena 2013 (PMNP2013)

NASA Astrophysics Data System (ADS)

Konopelchenko, B. G.; Landolfi, G.; Martina, L.; Vitolo, R.

2014-03-01

Modern theory of nonlinear integrable equations is nowdays an important and effective tool of study for numerous nonlinear phenomena in various branches of physics from hydrodynamics and optics to quantum filed theory and gravity. It includes the study of nonlinear partial differential and discrete equations, regular and singular behaviour of their solutions, Hamitonian and bi- Hamitonian structures, their symmetries, associated deformations of algebraic and geometrical structures with applications to various models in physics and mathematics. The PMNP 2013 conference focused on recent advances and developments in Continuous and discrete, classical and quantum integrable systems Hamiltonian, critical and geometric structures of nonlinear integrable equations Integrable systems in quantum field theory and matrix models Models of nonlinear phenomena in physics Applications of nonlinear integrable systems in physics The Scientific Committee of the conference was formed by Francesco Calogero (University of Rome `La Sapienza', Italy) Boris A Dubrovin (SISSA, Italy) Yuji Kodama (Ohio State University, USA) Franco Magri (University of Milan `Bicocca', Italy) Vladimir E Zakharov (University of Arizona, USA, and Landau Institute for Theoretical Physics, Russia) The Organizing Committee: Boris G Konopelchenko, Giulio Landolfi, Luigi Martina, Department of Mathematics and Physics `E De Giorgi' and the Istituto Nazionale di Fisica Nucleare, and Raffaele Vitolo, Department of Mathematics and Physics `E De Giorgi'. A list of sponsors, speakers, talks, participants and the conference photograph are given in the PDF. Conference photograph

Modeling of mid-infrared quantum cascade lasers: The role of temperature and operating field strength on the laser performance

NASA Astrophysics Data System (ADS)

Yousefvand, Hossein Reza

2017-07-01

In this paper a self-consistent numerical approach to study the temperature and bias dependent characteristics of mid-infrared (mid-IR) quantum cascade lasers (QCLs) is presented which integrates a number of quantum mechanical models. The field-dependent laser parameters including the nonradiative scattering times, the detuning and energy levels, the escape activation energy, the backfilling excitation energy and dipole moment of the optical transition are calculated for a wide range of applied electric fields by a self-consistent solution of Schrodinger-Poisson equations. A detailed analysis of performance of the obtained structure is carried out within a self-consistent solution of the subband population rate equations coupled with carrier coherent transport equations through the sequential resonant tunneling, by taking into account the temperature and bias dependency of the relevant parameters. Furthermore, the heat transfer equation is included in order to calculate the carrier temperature inside the active region levels. This leads to a compact predictive model to analyze the temperature and electric field dependent characteristics of the mid-IR QCLs such as the light-current (L-I), electric field-current (F-I) and core temperature-electric field (T-F) curves. For a typical mid-IR QCL, a good agreement was found between the simulated temperature-dependent L-I characteristic and experimental data, which confirms validity of the model. It is found that the main characteristics of the device such as output power and turn-on delay time are degraded by interplay between the temperature and Stark effects.

Towards a theory of cortical columns: From spiking neurons to interacting neural populations of finite size

PubMed Central

Gerstner, Wulfram

2017-01-01

Neural population equations such as neural mass or field models are widely used to study brain activity on a large scale. However, the relation of these models to the properties of single neurons is unclear. Here we derive an equation for several interacting populations at the mesoscopic scale starting from a microscopic model of randomly connected generalized integrate-and-fire neuron models. Each population consists of 50–2000 neurons of the same type but different populations account for different neuron types. The stochastic population equations that we find reveal how spike-history effects in single-neuron dynamics such as refractoriness and adaptation interact with finite-size fluctuations on the population level. Efficient integration of the stochastic mesoscopic equations reproduces the statistical behavior of the population activities obtained from microscopic simulations of a full spiking neural network model. The theory describes nonlinear emergent dynamics such as finite-size-induced stochastic transitions in multistable networks and synchronization in balanced networks of excitatory and inhibitory neurons. The mesoscopic equations are employed to rapidly integrate a model of a cortical microcircuit consisting of eight neuron types, which allows us to predict spontaneous population activities as well as evoked responses to thalamic input. Our theory establishes a general framework for modeling finite-size neural population dynamics based on single cell and synapse parameters and offers an efficient approach to analyzing cortical circuits and computations. PMID:28422957

Nonlinear resonance of the rotating circular plate under static loads in magnetic field

NASA Astrophysics Data System (ADS)

Hu, Yuda; Wang, Tong

2015-11-01

The rotating circular plate is widely used in mechanical engineering, meanwhile the plates are often in the electromagnetic field in modern industry with complex loads. In order to study the resonance of a rotating circular plate under static loads in magnetic field, the nonlinear vibration equation about the spinning circular plate is derived according to Hamilton principle. The algebraic expression of the initial deflection and the magneto elastic forced disturbance differential equation are obtained through the application of Galerkin integral method. By mean of modified Multiple scale method, the strongly nonlinear amplitude-frequency response equation in steady state is established. The amplitude frequency characteristic curve and the relationship curve of amplitude changing with the static loads and the excitation force of the plate are obtained according to the numerical calculation. The influence of magnetic induction intensity, the speed of rotation and the static loads on the amplitude and the nonlinear characteristics of the spinning plate are analyzed. The proposed research provides the theory reference for the research of nonlinear resonance of rotating plates in engineering.

Hydromagnetic flow of a Cu-water nanofluid past a moving wedge with viscous dissipation

NASA Astrophysics Data System (ADS)

M. Salem, A.; Galal, Ismail; Rania, Fathy

2014-04-01

A numerical study is performed to investigate the flow and heat transfer at the surface of a permeable wedge immersed in a copper (Cu)-water-based nanofluid in the presence of magnetic field and viscous dissipation using a nanofluid model proposed by Tiwari and Das (Tiwari I K and Das M K 2007 Int. J. Heat Mass Transfer 50 2002). A similarity solution for the transformed governing equation is obtained, and those equations are solved by employing a numerical shooting technique with a fourth-order Runge-Kutta integration scheme. A comparison with previously published work is carried out and shows that they are in good agreement with each other. The effects of velocity ratio parameter λ, solid volume fraction φ, magnetic field M, viscous dissipation Ec, and suction parameter Fw on the fluid flow and heat transfer characteristics are discussed. The unique and dual solutions for self-similar equations of the flow and heat transfer are analyzed numerically. Moreover, the range of the velocity ratio parameter for which the solution exists increases in the presence of magnetic field and suction parameter.

A multivariate variational objective analysis-assimilation method. Part 1: Development of the basic model

NASA Technical Reports Server (NTRS)

Achtemeier, Gary L.; Ochs, Harry T., III

1988-01-01

The variational method of undetermined multipliers is used to derive a multivariate model for objective analysis. The model is intended for the assimilation of 3-D fields of rawinsonde height, temperature and wind, and mean level temperature observed by satellite into a dynamically consistent data set. Relative measurement errors are taken into account. The dynamic equations are the two nonlinear horizontal momentum equations, the hydrostatic equation, and an integrated continuity equation. The model Euler-Lagrange equations are eleven linear and/or nonlinear partial differential and/or algebraic equations. A cyclical solution sequence is described. Other model features include a nonlinear terrain-following vertical coordinate that eliminates truncation error in the pressure gradient terms of the horizontal momentum equations and easily accommodates satellite observed mean layer temperatures in the middle and upper troposphere. A projection of the pressure gradient onto equivalent pressure surfaces removes most of the adverse impacts of the lower coordinate surface on the variational adjustment.

Exact solution of two collinear cracks normal to the boundaries of a 1D layered hexagonal piezoelectric quasicrystal

NASA Astrophysics Data System (ADS)

Zhou, Y.-B.; Li, X.-F.

2018-07-01

The electroelastic problem related to two collinear cracks of equal length and normal to the boundaries of a one-dimensional hexagonal piezoelectric quasicrystal layer is analysed. By using the finite Fourier transform, a mixed boundary value problem is solved when antiplane mechanical loading and inplane electric loading are applied. The problem is reduce to triple series equations, which are then transformed to a singular integral equation. For uniform remote loading, an exact solution is obtained in closed form, and explicit expressions for the electroelastic field are determined. The intensity factors of the electroelastic field and the energy release rate at the inner and outer crack tips are given and presented graphically.

Gaussian-reflectivity mirror resonator for a high-power transverse-flow CO2 laser.

PubMed

Ling, Dongxiong; Chen, Junruo; Li, Junchang

2006-05-01

A Gaussian-reflectivity mirror resonator is proposed to achieve high-quality laser beams. To analyze the laser fields in a Gaussian-reflectivity mirror resonator, the diffraction integral equations of a Gaussian-reflectivity mirror resonator are converted to the finite-sum matrix equations. Consequently, according to the Fox-Li laser self-reproducing principle, we describe the mode fields and their losses in the proposed resonator as eigenvectors and eigenvalues of a transfer matrix. The conclusion can be drawn from the numerical results that, if a Gaussian-reflectivity mirror is adopted for a plano-concave resonator, a fundamental mode can easily be obtained from a transverse-flow CO2 laser and high-quality laser beams can be expected.

Isogeometric Analysis of Boundary Integral Equations

DTIC Science & Technology

2015-04-21

methods, IgA relies on Non-Uniform Rational B- splines (NURBS) [43, 46], T- splines [55, 53] or subdivision surfaces [21, 48, 51] rather than piece- wise...structural dynamics [25, 26], plates and shells [15, 16, 27, 28, 37, 22, 23], phase-field models [17, 32, 33], and shape optimization [40, 41, 45, 59...polynomials for approximating the geometry and field variables. Thus, by replacing piecewise polynomials with NURBS or T- splines , one can develop

Nonlinear Relaxation in Population Dynamics

NASA Astrophysics Data System (ADS)

Cirone, Markus A.; de Pasquale, Ferdinando; Spagnolo, Bernardo

We analyze the nonlinear relaxation of a complex ecosystem composed of many interacting species. The ecological system is described by generalized Lotka-Volterra equations with a multiplicative noise. The transient dynamics is studied in the framework of the mean field theory and with random interaction between the species. We focus on the statistical properties of the asymptotic behaviour of the time integral of the ith population and on the distribution of the population and of the local field.

Calculation of plasma dielectric response in inhomogeneous magnetic field near electron cyclotron resonance

NASA Astrophysics Data System (ADS)

Evstatiev, Evstati; Svidzinski, Vladimir; Spencer, Andy; Galkin, Sergei

2014-10-01

Full wave 3-D modeling of RF fields in hot magnetized nonuniform plasma requires calculation of nonlocal conductivity kernel describing the dielectric response of such plasma to the RF field. In many cases, the conductivity kernel is a localized function near the test point which significantly simplifies numerical solution of the full wave 3-D problem. Preliminary results of feasibility analysis of numerical calculation of the conductivity kernel in a 3-D hot nonuniform magnetized plasma in the electron cyclotron frequency range will be reported. This case is relevant to modeling of ECRH in ITER. The kernel is calculated by integrating the linearized Vlasov equation along the unperturbed particle's orbits. Particle's orbits in the nonuniform equilibrium magnetic field are calculated numerically by one of the Runge-Kutta methods. RF electric field is interpolated on a specified grid on which the conductivity kernel is discretized. The resulting integrals in the particle's initial velocity and time are then calculated numerically. Different optimization approaches of the integration are tested in this feasibility analysis. Work is supported by the U.S. DOE SBIR program.

Nonlinear analysis of thermally and electrically actuated functionally graded material microbeam.

PubMed

Li, Yingli; Meguid, S A; Fu, Yiming; Xu, Daolin

2014-02-08

In this paper, we provide a unified and self-consistent treatment of a functionally graded material (FGM) microbeam with varying thermal conductivity subjected to non-uniform or uniform temperature field. Specifically, it is our objective to determine the effect of the microscopic size of the beam, the electrostatic gap, the temperature field and material property on the pull-in voltage of the microbeam under different boundary conditions. The non-uniform temperature field is obtained by integrating the steady-state heat conduction equation. The governing equations account for the microbeam size by introducing an internal material length-scale parameter that is based on the modified couple stress theory. Furthermore, it takes into account Casimir and van der Waals forces, and the associated electrostatic force with the first-order fringing field effects. The resulting nonlinear differential equations were converted to a coupled system of algebraic equations using the differential quadrature method. The outcome of our work shows the dramatic effect and dependence of the pull-in voltage of the FGM microbeam upon the temperature field, its gradient for a given boundary condition. Specifically, both uniform and non-uniform thermal loading can actuate the FGM microbeam even without an applied voltage. Our work also reveals that the non-uniform temperature field is more effective than the uniform temperature field in actuating a FGM cantilever-type microbeam. For the clamped-clamped case, care must be taken to account for the effective use of thermal loading in the design of microbeams. It is also observed that uniform thermal loading will lead to a reduction in the pull-in voltage of a FGM microbeam for all the three boundary conditions considered.

Comparison of the Effect of Horizontal Vibrations on Interfacial Waves in a Two-Layer System of Inviscid Liquids to Effective Gravity Inversion

NASA Astrophysics Data System (ADS)

Pimenova, Anastasiya V.; Goldobin, Denis S.; Lyubimova, Tatyana P.

2018-02-01

We study the waves at the interface between two thin horizontal layers of immiscible liquids subject to high-frequency tangential vibrations. Nonlinear governing equations are derived for the cases of two- and three-dimensional flows and arbitrary ratio of layer thicknesses. The derivation is performed within the framework of the long-wavelength approximation, which is relevant as the linear instability of a thin-layers system is long-wavelength. The dynamics of equations is integrable and the equations themselves can be compared to the Boussinesq equation for the gravity waves in shallow water, which allows one to compare the action of the vibrational field to the action of the gravity and its possible effective inversion.

Symmetry Analysis of Gauge-Invariant Field Equations via a Generalized Harrison-Estabrook Formalism.

NASA Astrophysics Data System (ADS)

Papachristou, Costas J.

The Harrison-Estabrook formalism for the study of invariance groups of partial differential equations is generalized and extended to equations that define, through their solutions, sections on vector bundles of various kinds. Applications include the Dirac, Yang-Mills, and self-dual Yang-Mills (SDYM) equations. The latter case exhibits interesting connections between the internal symmetries of SDYM and the existence of integrability characteristics such as a linear ("inverse scattering") system and Backlund transformations (BT's). By "verticalizing" the generators of coordinate point transformations of SDYM, nine nonlocal, generalized (as opposed to local, point) symmetries are constructed. The observation is made that the prolongations of these symmetries are parametric BT's for SDYM. It is thus concluded that the entire point group of SDYM contributes, upon verticalization, BT's to the system.

Fracture and fatigue analysis of functionally graded and homogeneous materials using singular integral equation approach

NASA Astrophysics Data System (ADS)

Zhao, Huaqing

There are two major objectives of this thesis work. One is to study theoretically the fracture and fatigue behavior of both homogeneous and functionally graded materials, with or without crack bridging. The other is to further develop the singular integral equation approach in solving mixed boundary value problems. The newly developed functionally graded materials (FGMs) have attracted considerable research interests as candidate materials for structural applications ranging from aerospace to automobile to manufacturing. From the mechanics viewpoint, the unique feature of FGMs is that their resistance to deformation, fracture and damage varies spatially. In order to guide the microstructure selection and the design and performance assessment of components made of functionally graded materials, in this thesis work, a series of theoretical studies has been carried out on the mode I stress intensity factors and crack opening displacements for FGMs with different combinations of geometry and material under various loading conditions, including: (1) a functionally graded layer under uniform strain, far field pure bending and far field axial loading, (2) a functionally graded coating on an infinite substrate under uniform strain, and (3) a functionally graded coating on a finite substrate under uniform strain, far field pure bending and far field axial loading. In solving crack problems in homogeneous and non-homogeneous materials, a very powerful singular integral equation (SEE) method has been developed since 1960s by Erdogan and associates to solve mixed boundary value problems. However, some of the kernel functions developed earlier are incomplete and possibly erroneous. In this thesis work, mode I fracture problems in a homogeneous strip are reformulated and accurate singular Cauchy type kernels are derived. Very good convergence rates and consistency with standard data are achieved. Other kernel functions are subsequently developed for mode I fracture in functionally graded materials. This work provides a solid foundation for further applications of the singular integral equation approach to fracture and fatigue problems in advanced composites. The concept of crack bridging is a unifying theory for fracture at various length scales, from atomic cleavage to rupture of concrete structures. However, most of the previous studies are limited to small scale bridging analyses although large scale bridging conditions prevail in engineering materials. In this work, a large scale bridging analysis is included within the framework of singular integral equation approach. This allows us to study fracture, fatigue and toughening mechanisms in advanced materials with crack bridging. As an example, the fatigue crack growth of grain bridging ceramics is studied. With the advent of composite materials technology, more complex material microstructures are being introduced, and more mechanics issues such as inhomogeneity and nonlinearity come into play. Improved mathematical and numerical tools need to be developed to allow theoretical modeling of these materials. This thesis work is an attempt to meet these challenges by making contributions to both micromechanics modeling and applied mathematics. It sets the stage for further investigations of a wide range of problems in the deformation and fracture of advanced engineering materials.

Transient Effects in Planar Solidification of Dilute Binary Alloys

NASA Technical Reports Server (NTRS)

Mazuruk, Konstantin; Volz, Martin P.

2008-01-01

The initial transient during planar solidification of dilute binary alloys is studied in the framework of the boundary integral method that leads to the non-linear Volterra integral governing equation. An analytical solution of this equation is obtained for the case of a constant growth rate which constitutes the well-known Tiller's formula for the solute transient. The more physically relevant, constant ramping down temperature case has been studied both numerically and analytically. In particular, an asymptotic analytical solution is obtained for the initial transient behavior. A numerical technique to solve the non-linear Volterra equation is developed and the solution is obtained for a family of the governing parameters. For the rapid solidification condition, growth rate spikes have been observed even for the infinite kinetics model. When recirculating fluid flow is included into the analysis, the spike feature is dramatically diminished. Finally, we have investigated planar solidification with a fluctuating temperature field as a possible mechanism for frequently observed solute trapping bands.

Function-Space-Based Solution Scheme for the Size-Modified Poisson-Boltzmann Equation in Full-Potential DFT.

PubMed

Ringe, Stefan; Oberhofer, Harald; Hille, Christoph; Matera, Sebastian; Reuter, Karsten

2016-08-09

The size-modified Poisson-Boltzmann (MPB) equation is an efficient implicit solvation model which also captures electrolytic solvent effects. It combines an account of the dielectric solvent response with a mean-field description of solvated finite-sized ions. We present a general solution scheme for the MPB equation based on a fast function-space-oriented Newton method and a Green's function preconditioned iterative linear solver. In contrast to popular multigrid solvers, this approach allows us to fully exploit specialized integration grids and optimized integration schemes. We describe a corresponding numerically efficient implementation for the full-potential density-functional theory (DFT) code FHI-aims. We show that together with an additional Stern layer correction the DFT+MPB approach can describe the mean activity coefficient of a KCl aqueous solution over a wide range of concentrations. The high sensitivity of the calculated activity coefficient on the employed ionic parameters thereby suggests to use extensively tabulated experimental activity coefficients of salt solutions for a systematic parametrization protocol.

Integral representations of solutions of the wave equation based on relativistic wavelets

NASA Astrophysics Data System (ADS)

Perel, Maria; Gorodnitskiy, Evgeny

2012-09-01

A representation of solutions of the wave equation with two spatial coordinates in terms of localized elementary ones is presented. Elementary solutions are constructed from four solutions with the help of transformations of the affine Poincaré group, i.e. with the help of translations, dilations in space and time and Lorentz transformations. The representation can be interpreted in terms of the initial-boundary value problem for the wave equation in a half-plane. It gives the solution as an integral representation of two types of solutions: propagating localized solutions running away from the boundary under different angles and packet-like surface waves running along the boundary and exponentially decreasing away from the boundary. Properties of elementary solutions are discussed. A numerical investigation of coefficients of the decomposition is carried out. An example of the decomposition of the field created by sources moving along a line with different speeds is considered, and the dependence of coefficients on speeds of sources is discussed.

A new integrable equation combining the modified KdV equation with the negative-order modified KdV equation: multiple soliton solutions and a variety of solitonic solutions

NASA Astrophysics Data System (ADS)

Wazwaz, Abdul-Majid

2018-07-01

A new third-order integrable equation is constructed via combining the recursion operator of the modified KdV equation (MKdV) and its inverse recursion operator. The developed equation will be termed the modified KdV-negative order modified KdV equation (MKdV-nMKdV). The complete integrability of this equation is confirmed by showing that it nicely possesses the Painlevé property. We obtain multiple soliton solutions for the newly developed integrable equation. Moreover, this equation enjoys a variety of solutions which include solitons, peakons, cuspons, negaton, positon, complexiton and other solutions.

A coupled-mode theory for multiwaveguide systems satisfying the reciprocity theorem and power conservation

NASA Technical Reports Server (NTRS)

Chuang, Shun-Lien

1987-01-01

Two sets of coupled-mode equations for multiwaveguide systems are derived using a generalized reciprocity relation; one set for a lossless system, and the other for a general lossy or lossless system. The second set of equations also reduces to those of the first set in the lossless case under the condition that the transverse field components are chosen to be real. Analytical relations between the coupling coefficients are shown and applied to the coupling of mode equations. It is shown analytically that these results satisfy exactly both the reciprocity theorem and power conservation. New orthogonal relations between the supermodes are derived in matrix form, with the overlap integrals taken into account.

Ring Current Ion Coupling with Electromagnetic Ion Cyclotron Waves

NASA Technical Reports Server (NTRS)

Khazanov. G. V.; Gamayunov, K. V.; Jordanova, V. K.; Six, N. Frank (Technical Monitor)

2002-01-01

A new ring current global model has been developed that couples the system of two kinetic equations: one equation describes the ring current (RC) ion dynamic, and another equation describes wave evolution of electromagnetic ion cyclotron waves (EMIC). The coupled model is able to simulate, for the first time self-consistently calculated RC ion kinetic and evolution of EMIC waves that propagate along geomagnetic field lines and reflect from the ionosphere. Ionospheric properties affect the reflection index through the integral Pedersen and Hall conductivities. The structure and dynamics of the ring current proton precipitating flux regions, intensities of EMIC global RC energy balance, and some other parameters will be studied in detail for the selected geomagnetic storms.

Annual Review of Progress in Applied Computational Electromagnetics (5th), Held in Monterey, California on March 20-24 1989

DTIC Science & Technology

1989-01-01

circuit of the field equations of Maxwell ", Proc IRE, vol 32, Kay 1944, pp 360-367. 3. S. Akhtarzad P.B. Johns ,"Solution of Maxwell’s equations in three...ELFCTROMAGNETICS APPLIED TO INTEGRATED CIRCUIT MICROLITHOGRAPHY AND METROLOGY John C . Mould Jr. & Gregory L Wojc* Welinger Associates, 4410 El Camino Real, Los...1AICROLITHOGRAPHY AND METROLOGY John C . Mould Jr. & Gregory L Wo c * Weldlinger Associates, 4410 El Camino Real. Los Allos, Ca. 94022 1. Pholoreslat

Euclidean black hole vortices

NASA Technical Reports Server (NTRS)

Dowker, Fay; Gregory, Ruth; Traschen, Jennie

1991-01-01

We argue the existence of solutions of the Euclidean Einstein equations that correspond to a vortex sitting at the horizon of a black hole. We find the asymptotic behaviors, at the horizon and at infinity, of vortex solutions for the gauge and scalar fields in an abelian Higgs model on a Euclidean Schwarzschild background and interpolate between them by integrating the equations numerically. Calculating the backreaction shows that the effect of the vortex is to cut a slice out of the Schwarzschild geometry. Consequences of these solutions for black hole thermodynamics are discussed.

Relativistic Kinetic Theory

NASA Astrophysics Data System (ADS)

Vereshchagin, Gregory V.; Aksenov, Alexey G.

2017-02-01

Preface; Acknowledgements; Acronyms and definitions; Introduction; Part I. Theoretical Foundations: 1. Basic concepts; 2. Kinetic equation; 3. Averaging; 4. Conservation laws and equilibrium; 5. Relativistic BBGKY hierarchy; 6. Basic parameters in gases and plasmas; Part II. Numerical Methods: 7. The basics of computational physics; 8. Direct integration of Boltzmann equations; 9. Multidimensional hydrodynamics; Part III. Applications: 10. Wave dispersion in relativistic plasma; 11. Thermalization in relativistic plasma; 12. Kinetics of particles in strong fields; 13. Compton scattering in astrophysics and cosmology; 14. Self-gravitating systems; 15. Neutrinos, gravitational collapse and supernovae; Appendices; Bibliography; Index.

Discretization of the induced-charge boundary integral equation.

PubMed

Bardhan, Jaydeep P; Eisenberg, Robert S; Gillespie, Dirk

2009-07-01

Boundary-element methods (BEMs) for solving integral equations numerically have been used in many fields to compute the induced charges at dielectric boundaries. In this paper, we consider a more accurate implementation of BEM in the context of ions in aqueous solution near proteins, but our results are applicable more generally. The ions that modulate protein function are often within a few angstroms of the protein, which leads to the significant accumulation of polarization charge at the protein-solvent interface. Computing the induced charge accurately and quickly poses a numerical challenge in solving a popular integral equation using BEM. In particular, the accuracy of simulations can depend strongly on seemingly minor details of how the entries of the BEM matrix are calculated. We demonstrate that when the dielectric interface is discretized into flat tiles, the qualocation method of Tausch [IEEE Trans Comput.-Comput.-Aided Des. 20, 1398 (2001)] to compute the BEM matrix elements is always more accurate than the traditional centroid-collocation method. Qualocation is not more expensive to implement than collocation and can save significant computational time by reducing the number of boundary elements needed to discretize the dielectric interfaces.

Inverse scattering transform analysis of rogue waves using local periodization procedure

NASA Astrophysics Data System (ADS)

Randoux, Stéphane; Suret, Pierre; El, Gennady

2016-07-01

The nonlinear Schrödinger equation (NLSE) stands out as the dispersive nonlinear partial differential equation that plays a prominent role in the modeling and understanding of the wave phenomena relevant to many fields of nonlinear physics. The question of random input problems in the one-dimensional and integrable NLSE enters within the framework of integrable turbulence, and the specific question of the formation of rogue waves (RWs) has been recently extensively studied in this context. The determination of exact analytic solutions of the focusing 1D-NLSE prototyping RW events of statistical relevance is now considered as the problem of central importance. Here we address this question from the perspective of the inverse scattering transform (IST) method that relies on the integrable nature of the wave equation. We develop a conceptually new approach to the RW classification in which appropriate, locally coherent structures are specifically isolated from a globally incoherent wave train to be subsequently analyzed by implementing a numerical IST procedure relying on a spatial periodization of the object under consideration. Using this approach we extend the existing classifications of the prototypes of RWs from standard breathers and their collisions to more general nonlinear modes characterized by their nonlinear spectra.

Discretization of the induced-charge boundary integral equation

NASA Astrophysics Data System (ADS)

Bardhan, Jaydeep P.; Eisenberg, Robert S.; Gillespie, Dirk

2009-07-01

Boundary-element methods (BEMs) for solving integral equations numerically have been used in many fields to compute the induced charges at dielectric boundaries. In this paper, we consider a more accurate implementation of BEM in the context of ions in aqueous solution near proteins, but our results are applicable more generally. The ions that modulate protein function are often within a few angstroms of the protein, which leads to the significant accumulation of polarization charge at the protein-solvent interface. Computing the induced charge accurately and quickly poses a numerical challenge in solving a popular integral equation using BEM. In particular, the accuracy of simulations can depend strongly on seemingly minor details of how the entries of the BEM matrix are calculated. We demonstrate that when the dielectric interface is discretized into flat tiles, the qualocation method of Tausch [IEEE Trans Comput.-Comput.-Aided Des. 20, 1398 (2001)] to compute the BEM matrix elements is always more accurate than the traditional centroid-collocation method. Qualocation is not more expensive to implement than collocation and can save significant computational time by reducing the number of boundary elements needed to discretize the dielectric interfaces.

A Fast Solver for Implicit Integration of the Vlasov--Poisson System in the Eulerian Framework

DOE Office of Scientific and Technical Information (OSTI.GOV)

Garrett, C. Kristopher; Hauck, Cory D.

In this paper, we present a domain decomposition algorithm to accelerate the solution of Eulerian-type discretizations of the linear, steady-state Vlasov equation. The steady-state solver then forms a key component in the implementation of fully implicit or nearly fully implicit temporal integrators for the nonlinear Vlasov--Poisson system. The solver relies on a particular decomposition of phase space that enables the use of sweeping techniques commonly used in radiation transport applications. The original linear system for the phase space unknowns is then replaced by a smaller linear system involving only unknowns on the boundary between subdomains, which can then be solvedmore » efficiently with Krylov methods such as GMRES. Steady-state solves are combined to form an implicit Runge--Kutta time integrator, and the Vlasov equation is coupled self-consistently to the Poisson equation via a linearized procedure or a nonlinear fixed-point method for the electric field. Finally, numerical results for standard test problems demonstrate the efficiency of the domain decomposition approach when compared to the direct application of an iterative solver to the original linear system.« less

Inverse scattering transform analysis of rogue waves using local periodization procedure

PubMed Central

Randoux, Stéphane; Suret, Pierre; El, Gennady

2016-01-01

The nonlinear Schrödinger equation (NLSE) stands out as the dispersive nonlinear partial differential equation that plays a prominent role in the modeling and understanding of the wave phenomena relevant to many fields of nonlinear physics. The question of random input problems in the one-dimensional and integrable NLSE enters within the framework of integrable turbulence, and the specific question of the formation of rogue waves (RWs) has been recently extensively studied in this context. The determination of exact analytic solutions of the focusing 1D-NLSE prototyping RW events of statistical relevance is now considered as the problem of central importance. Here we address this question from the perspective of the inverse scattering transform (IST) method that relies on the integrable nature of the wave equation. We develop a conceptually new approach to the RW classification in which appropriate, locally coherent structures are specifically isolated from a globally incoherent wave train to be subsequently analyzed by implementing a numerical IST procedure relying on a spatial periodization of the object under consideration. Using this approach we extend the existing classifications of the prototypes of RWs from standard breathers and their collisions to more general nonlinear modes characterized by their nonlinear spectra. PMID:27385164

Volume integral equation for electromagnetic scattering: Rigorous derivation and analysis for a set of multilayered particles with piecewise-smooth boundaries in a passive host medium

NASA Astrophysics Data System (ADS)

Yurkin, Maxim A.; Mishchenko, Michael I.

2018-04-01

We present a general derivation of the frequency-domain volume integral equation (VIE) for the electric field inside a nonmagnetic scattering object from the differential Maxwell equations, transmission boundary conditions, radiation condition at infinity, and locally-finite-energy condition. The derivation applies to an arbitrary spatially finite group of particles made of isotropic materials and embedded in a passive host medium, including those with edges, corners, and intersecting internal interfaces. This is a substantially more general type of scatterer than in all previous derivations. We explicitly treat the strong singularity of the integral kernel, but keep the entire discussion accessible to the applied scattering community. We also consider the known results on the existence and uniqueness of VIE solution and conjecture a general sufficient condition for that. Finally, we discuss an alternative way of deriving the VIE for an arbitrary object by means of a continuous transformation of the everywhere smooth refractive-index function into a discontinuous one. Overall, the paper examines and pushes forward the state-of-the-art understanding of various analytical aspects of the VIE.

A Fast Solver for Implicit Integration of the Vlasov--Poisson System in the Eulerian Framework

DOE PAGES

Garrett, C. Kristopher; Hauck, Cory D.

2018-04-05

In this paper, we present a domain decomposition algorithm to accelerate the solution of Eulerian-type discretizations of the linear, steady-state Vlasov equation. The steady-state solver then forms a key component in the implementation of fully implicit or nearly fully implicit temporal integrators for the nonlinear Vlasov--Poisson system. The solver relies on a particular decomposition of phase space that enables the use of sweeping techniques commonly used in radiation transport applications. The original linear system for the phase space unknowns is then replaced by a smaller linear system involving only unknowns on the boundary between subdomains, which can then be solvedmore » efficiently with Krylov methods such as GMRES. Steady-state solves are combined to form an implicit Runge--Kutta time integrator, and the Vlasov equation is coupled self-consistently to the Poisson equation via a linearized procedure or a nonlinear fixed-point method for the electric field. Finally, numerical results for standard test problems demonstrate the efficiency of the domain decomposition approach when compared to the direct application of an iterative solver to the original linear system.« less

Stability: Conservation laws, Painlevé analysis and exact solutions for S-KP equation in coupled dusty plasma

NASA Astrophysics Data System (ADS)

EL-Kalaawy, O. H.; Moawad, S. M.; Wael, Shrouk

The propagation of nonlinear waves in unmagnetized strongly coupled dusty plasma with Boltzmann distributed electrons, iso-nonthermal distributed ions and negatively charged dust grains is considered. The basic set of fluid equations is reduced to the Schamel Kadomtsev-Petviashvili (S-KP) equation by using the reductive perturbation method. The variational principle and conservation laws of S-KP equation are obtained. It is shown that the S-KP equation is non-integrable using Painlevé analysis. A set of new exact solutions are obtained by auto-Bäcklund transformations. The stability analysis is discussed for the existence of dust acoustic solitary waves (DASWs) and it is found that the physical parameters have strong effects on the stability criterion. In additional to, the electric field and the true Mach number of this solution are investigated. Finally, we will study the physical meanings of solutions.

The applicability of turbulence models to aerodynamic and propulsion flowfields at McDonnell-Douglas Aerospace

NASA Technical Reports Server (NTRS)

Kral, Linda D.; Ladd, John A.; Mani, Mori

1995-01-01

The objective of this viewgraph presentation is to evaluate turbulence models for integrated aircraft components such as the forebody, wing, inlet, diffuser, nozzle, and afterbody. The one-equation models have replaced the algebraic models as the baseline turbulence models. The Spalart-Allmaras one-equation model consistently performs better than the Baldwin-Barth model, particularly in the log-layer and free shear layers. Also, the Sparlart-Allmaras model is not grid dependent like the Baldwin-Barth model. No general turbulence model exists for all engineering applications. The Spalart-Allmaras one-equation model and the Chien k-epsilon models are the preferred turbulence models. Although the two-equation models often better predict the flow field, they may take from two to five times the CPU time. Future directions are in further benchmarking the Menter blended k-w/k-epsilon and algorithmic improvements to reduce CPU time of the two-equation model.

A Super mKdV Equation: Bosonization, Painlevé Property and Exact Solutions

NASA Astrophysics Data System (ADS)

Ren, Bo; Lou, Sen-Yue

2018-04-01

The symmetry of the fermionic field is obtained by means of the Lax pair of the mKdV equation. A new super mKdV equation is constructed by virtue of the symmetry of the fermionic form. The super mKdV system is changed to a system of coupled bosonic equations with the bosonization approach. The bosonized SmKdV (BSmKdV) equation admits Painlevé property by the standard singularity analysis. The traveling wave solutions of the BSmKdV system are presented by the mapping and deformation method. We also provide other ideas to construct new super integrable systems. Supported by the National Natural Science Foundation of China under Grant Nos. 11775146, 11435005, and 11472177, Shanghai Knowledge Service Platform for Trustworthy Internet of Things under Grant No. ZF1213 and K. C. Wong Magna Fund in Ningbo University

Phase-resolved fluid dynamic forces of a flapping foil energy harvester based on PIV measurements

NASA Astrophysics Data System (ADS)

Liburdy, James

2017-11-01

Two-dimensional particle image velocimetry measurements are performed in a wind tunnel to evaluate the spatial and temporal fluid dynamic forces acting on a flapping foil operating in the energy harvesting regime. Experiments are conducted at reduced frequencies (k = fc/U) of 0.05 - 0.2, pitching angle of, and heaving amplitude of A / c = 0.6. The phase-averaged pressure field is obtained by integrating the pressure Poisson equation. Fluid dynamic forces are then obtained through the integral momentum equation. Results are compared with a simple force model based on the concept of flow impulse. These results help to show the detailed force distributions, their transient nature and aide in understanding the impact of the fluid flow structures that contribute to the power production.

A 2D electrostatic PIC code for the Mark III Hypercube

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ferraro, R.D.; Liewer, P.C.; Decyk, V.K.

We have implemented a 2D electrostastic plasma particle in cell (PIC) simulation code on the Caltech/JPL Mark IIIfp Hypercube. The code simulates plasma effects by evolving in time the trajectories of thousands to millions of charged particles subject to their self-consistent fields. Each particle`s position and velocity is advanced in time using a leap frog method for integrating Newton`s equations of motion in electric and magnetic fields. The electric field due to these moving charged particles is calculated on a spatial grid at each time by solving Poisson`s equation in Fourier space. These two tasks represent the largest part ofmore » the computation. To obtain efficient operation on a distributed memory parallel computer, we are using the General Concurrent PIC (GCPIC) algorithm previously developed for a 1D parallel PIC code.« less

Traction patterns of tumor cells.

PubMed

Ambrosi, D; Duperray, A; Peschetola, V; Verdier, C

2009-01-01

The traction exerted by a cell on a planar deformable substrate can be indirectly obtained on the basis of the displacement field of the underlying layer. The usual methodology used to address this inverse problem is based on the exploitation of the Green tensor of the linear elasticity problem in a half space (Boussinesq problem), coupled with a minimization algorithm under force penalization. A possible alternative strategy is to exploit an adjoint equation, obtained on the basis of a suitable minimization requirement. The resulting system of coupled elliptic partial differential equations is applied here to determine the force field per unit surface generated by T24 tumor cells on a polyacrylamide substrate. The shear stress obtained by numerical integration provides quantitative insight of the traction field and is a promising tool to investigate the spatial pattern of force per unit surface generated in cell motion, particularly in the case of such cancer cells.

Path-integral methods for analyzing the effects of fluctuations in stochastic hybrid neural networks.

PubMed

Bressloff, Paul C

2015-01-01

We consider applications of path-integral methods to the analysis of a stochastic hybrid model representing a network of synaptically coupled spiking neuronal populations. The state of each local population is described in terms of two stochastic variables, a continuous synaptic variable and a discrete activity variable. The synaptic variables evolve according to piecewise-deterministic dynamics describing, at the population level, synapses driven by spiking activity. The dynamical equations for the synaptic currents are only valid between jumps in spiking activity, and the latter are described by a jump Markov process whose transition rates depend on the synaptic variables. We assume a separation of time scales between fast spiking dynamics with time constant [Formula: see text] and slower synaptic dynamics with time constant τ. This naturally introduces a small positive parameter [Formula: see text], which can be used to develop various asymptotic expansions of the corresponding path-integral representation of the stochastic dynamics. First, we derive a variational principle for maximum-likelihood paths of escape from a metastable state (large deviations in the small noise limit [Formula: see text]). We then show how the path integral provides an efficient method for obtaining a diffusion approximation of the hybrid system for small ϵ. The resulting Langevin equation can be used to analyze the effects of fluctuations within the basin of attraction of a metastable state, that is, ignoring the effects of large deviations. We illustrate this by using the Langevin approximation to analyze the effects of intrinsic noise on pattern formation in a spatially structured hybrid network. In particular, we show how noise enlarges the parameter regime over which patterns occur, in an analogous fashion to PDEs. Finally, we carry out a [Formula: see text]-loop expansion of the path integral, and use this to derive corrections to voltage-based mean-field equations, analogous to the modified activity-based equations generated from a neural master equation.

Reduced Order Podolsky Model

NASA Astrophysics Data System (ADS)

Thibes, Ronaldo

2017-02-01

We perform the canonical and path integral quantizations of a lower-order derivatives model describing Podolsky's generalized electrodynamics. The physical content of the model shows an auxiliary massive vector field coupled to the usual electromagnetic field. The equivalence with Podolsky's original model is studied at classical and quantum levels. Concerning the dynamical time evolution, we obtain a theory with two first-class and two second-class constraints in phase space. We calculate explicitly the corresponding Dirac brackets involving both vector fields. We use the Senjanovic procedure to implement the second-class constraints and the Batalin-Fradkin-Vilkovisky path integral quantization scheme to deal with the symmetries generated by the first-class constraints. The physical interpretation of the results turns out to be simpler due to the reduced derivatives order permeating the equations of motion, Dirac brackets and effective action.

Using Vertically Integrated Ocean Fields to Characterize Greenland Icebergs' Distribution and Lifetime

NASA Astrophysics Data System (ADS)

Marson, Juliana M.; Myers, Paul G.; Hu, Xianmin; Le Sommer, Julien

2018-05-01

Icebergs represent approximately half of Greenland's yearly mass loss, having important implications for biological productivity, freshwater fluxes in the ocean, and navigation. This study applies an iceberg model that uses integrated ocean fields (from surface to iceberg keel) to simulate the drift and decay of Greenland icebergs. This version of iceberg model (VERT) is compared with a more widely adopted version (SURF) which only uses surface ocean fields in its equations. We show that icebergs in VERT tend to drift along the shelf break, while in SURF they concentrate along the coastline. Additionally, we show that Greenland's southeast coast is the source of ˜60% of the icebergs that cross the interior of the Labrador Sea—a region that stages buoyancy-driven convection and is, therefore, sensitive to freshwater input.

System analysis of plasma centrifuges and sputtering

NASA Technical Reports Server (NTRS)

Hong, S. H.

1978-01-01

System analyses of cylindrical plasma centrifuges are presented, for which the velocity field and electromagnetic fields are calculated. The effects of different electrode geometrics, induced magnetic fields, Hall-effect, and secondary flows are discussed. It is shown that speeds of 10000 m/sec can be achieved in plasma centrifuges, and that an efficient separation of U238 and U235 in uranium plasmas is feasible. The external boundary-value problem for the deposition of sputtering products is reduced to a Fredholm integral equation, which is solved analytically by means of the method of successive approximations.

Predicting the Rotor-Stator Interaction Acoustics of a Ducted Fan Engine

NASA Technical Reports Server (NTRS)

Biedron, Robert T.; Rumsey, Christopher L.; Podboy, Gary G.; Dunn, M. H.

2001-01-01

A Navier-Stokes computation is performed for a ducted-fan configuration with the goal of predicting rotor-stator noise generation without having to resort to heuristic modeling. The calculated pressure field in the inlet region is decomposed into classical infinite-duct modes, which are then used in either a hybrid finite-element/Kirchhoff surface method or boundary integral equation method to calculate the far field noise. Comparisons with experimental data are presented, including rotor wake surveys and far field sound pressure levels for two blade passage frequency (BPF) tones.

Coherent electromagnetic waves in the presence of a half space of randomly distributed scatterers

NASA Technical Reports Server (NTRS)

Karam, M. A.; Fung, A. K.

1988-01-01

The present investigation of coherent field propagation notes, upon solving the Foldy-Twersky integral equation for a half-space of small spherical scatterers illuminated by a plane wave at oblique incidence, that the coherent field for a horizontally-polarized incident wave exhibits reflectivity and transmissivity consistent with the Fresnel formula for an equivalent continuous effective medium. In the case of a vertically polarized incident wave, both the vertical and longitudinal waves obtained for the coherent field have reflectivities and transmissivities that do not agree with the Fresnel formula.

Unimodular Einstein-Cartan gravity: Dynamics and conservation laws

NASA Astrophysics Data System (ADS)

Bonder, Yuri; Corral, Cristóbal

2018-04-01

Unimodular gravity is an interesting approach to address the cosmological constant problem, since the vacuum energy density of quantum fields does not gravitate in this framework, and the cosmological constant appears as an integration constant. These features arise as a consequence of considering a constrained volume element 4-form that breaks the diffeomorphisms invariance down to volume preserving diffeomorphisms. In this work, the first-order formulation of unimodular gravity is presented by considering the spin density of matter fields as a source of spacetime torsion. Even though the most general matter Lagrangian allowed by the symmetries is considered, dynamical restrictions arise on their functional dependence. The field equations are obtained and the conservation laws associated with the symmetries are derived. It is found that, analogous to torsion-free unimodular gravity, the field equation for the vierbein is traceless; nevertheless, torsion is algebraically related to the spin density as in standard Einstein-Cartan theory. The particular example of massless Dirac spinors is studied, and comparisons with standard Einstein-Cartan theory are shown.

Spectral method for the static electric potential of a charge density in a composite medium

NASA Astrophysics Data System (ADS)

Bergman, David J.; Farhi, Asaf

2018-04-01

A spectral representation for the static electric potential field in a two-constituent composite medium is presented. A theory is developed for calculating the quasistatic eigenstates of Maxwell's equations for such a composite. The local physical potential field produced in the system by a given source charge density is expanded in this set of orthogonal eigenstates for any position r. The source charges can be located anywhere, i.e., inside any of the constituents. This is shown to work even if the eigenfunctions are normalized in an infinite volume. If the microstructure consists of a cluster of separate inclusions in a uniform host medium, then the quasistatic eigenstates of all the separate isolated inclusions can be used to calculate the eigenstates of the total structure as well as the local potential field. Once the eigenstates are known for a given host and a given microstructure, then calculation of the local field only involves calculating three-dimensional integrals of known functions and solving sets of linear algebraic equations.

Logarithmic violation of scaling in anisotropic kinematic dynamo model

NASA Astrophysics Data System (ADS)

Antonov, N. V.; Gulitskiy, N. M.

2016-01-01

Inertial-range asymptotic behavior of a vector (e.g., magnetic) field, passively advected by a strongly anisotropic turbulent flow, is studied by means of the field theoretic renormalization group and the operator product expansion. The advecting velocity field is Gaussian, not correlated in time, with the pair correlation function of the form ∝δ (t -t')/k⊥d-1 +ξ , where k⊥ = |k⊥| and k⊥ is the component of the wave vector, perpendicular to the distinguished direction. The stochastic advection-diffusion equation for the transverse (divergence-free) vector field includes, as special cases, the kinematic dynamo model for magnetohydrodynamic turbulence and the linearized Navier-Stokes equation. In contrast to the well known isotropic Kraichnan's model, where various correlation functions exhibit anomalous scaling behavior with infinite sets of anomalous exponents, here the dependence on the integral turbulence scale L has a logarithmic behavior: instead of power-like corrections to ordinary scaling, determined by naive (canonical) dimensions, the anomalies manifest themselves as polynomials of logarithms of L.

Chapman-Enskog expansion for the Vicsek model of self-propelled particles

NASA Astrophysics Data System (ADS)

Ihle, Thomas

2016-08-01

Using the standard Vicsek model, I show how the macroscopic transport equations can be systematically derived from microscopic collision rules. The approach starts with the exact evolution equation for the N-particle probability distribution and, after making the mean-field assumption of molecular chaos, leads to a multi-particle Enskog-type equation. This equation is treated by a non-standard Chapman-Enskog expansion to extract the macroscopic behavior. The expansion includes terms up to third order in a formal expansion parameter ɛ, and involves a fast time scale. A self-consistent closure of the moment equations is presented that leads to a continuity equation for the particle density and a Navier-Stokes-like equation for the momentum density. Expressions for all transport coefficients in these macroscopic equations are given explicitly in terms of microscopic parameters of the model. The transport coefficients depend on specific angular integrals which are evaluated asymptotically in the limit of infinitely many collision partners, using an analogy to a random walk. The consistency of the Chapman-Enskog approach is checked by an independent calculation of the shear viscosity using a Green-Kubo relation.

Quantum integrability and functional equations

NASA Astrophysics Data System (ADS)

Volin, Dmytro

2010-03-01

In this thesis a general procedure to represent the integral Bethe Ansatz equations in the form of the Reimann-Hilbert problem is given. This allows us to study in simple way integrable spin chains in the thermodynamic limit. Based on the functional equations we give the procedure that allows finding the subleading orders in the solution of various integral equations solved to the leading order by the Wiener-Hopf technics. The integral equations are studied in the context of the AdS/CFT correspondence, where their solution allows verification of the integrability conjecture up to two loops of the strong coupling expansion. In the context of the two-dimensional sigma models we analyze the large-order behavior of the asymptotic perturbative expansion. Obtained experience with the functional representation of the integral equations allowed us also to solve explicitly the crossing equations that appear in the AdS/CFT spectral problem.

A systematic study of finite BRST-BFV transformations in generalized Hamiltonian formalism

NASA Astrophysics Data System (ADS)

Batalin, Igor A.; Lavrov, Peter M.; Tyutin, Igor V.

2014-09-01

We study systematically finite BRST-BFV transformations in the generalized Hamiltonian formalism. We present explicitly their Jacobians and the form of a solution to the compensation equation determining the functional field dependence of finite Fermionic parameters, necessary to generate an arbitrary finite change of gauge-fixing functions in the path integral.

Finite BRST-BFV transformations for dynamical systems with second-class constraints

NASA Astrophysics Data System (ADS)

Batalin, Igor A.; Lavrov, Peter M.; Tyutin, Igor V.

2015-06-01

We study finite field-dependent BRST-BFV transformations for dynamical systems with first- and second-class constraints within the generalized Hamiltonian formalism. We find explicitly their Jacobians and the form of a solution to the compensation equation necessary for generating an arbitrary finite change of gauge-fixing functionals in the path integral.

Electromagnetic Scattering From a Polygonal Thin Metallic Plate Using Quadrilateral Meshing

NASA Technical Reports Server (NTRS)

Deshpande, Manohar D.

2003-01-01

The problem of electromagnetic (EM) scattering from irregularly shaped, thin, metallic flat plates in free space is solved using the electric field integral equation (EFIE) approach in conjunction with the method of moments (MoM) with quadrilateral meshing. An irregularly shaped thin plate is discretized into quadrilateral patches and the unknown electric surface current over the plate is expressed in terms of proper basis functions over these patches. The basis functions for the electric surface current density that satisfy the proper boundary conditions on these quadrilateral patches are derived. The unknown surface current density on these quadrilateral patches is determined by setting up and solving the electric field integral equation by the application of the MoM. From the knowledge of the surface current density, the EM scattering from various irregularly shaped plates is determined and compared with the earlier published results. The novelty in the present approach is the use of quadrilateral patches instead of well known and often used triangular patches. The numerical results obtained using the quadrilateral patches compare favorably with measured results.

Supercritical flow past a symmetrical bicircular arc airfoil

NASA Technical Reports Server (NTRS)

Holt, Maurice; Yew, Khoy Chuah

1989-01-01

A numerical scheme is developed for computing steady supercritical flow about symmetrical airfoils, applying it to an ellipse for zero angle of attack. An algorithmic description of this new scheme is presented. Application to a symmetrical bicircular arc airfoil is also proposed. The flow field before the shock is region 1. For transonic flow, singularity can be avoided by integrating the resulting ordinary differential equations away from the body. Region 2 contains the shock which will be located by shock fitting techniques. The shock divides region 2 into supersonic and subsonic regions and there is no singularity problem in this case. The Method of Lines is used in this region and it is advantageous to integrate the resulting ordinary differential equation along the body for shock fitting. Coaxial coordinates have to be used for the bicircular arc airfoil so that boundary values on the airfoil body can be taken with one direction of the coaxial coordinates fixed. To avoid taking boundary values at + or - infinity in the coaxial co-ordinary system, approximate analytical representation of the flow field near the tips of the airfoil is proposed.

Force-field parameters from the SAFT-γ equation of state for use in coarse-grained molecular simulations.

PubMed

Müller, Erich A; Jackson, George

2014-01-01

A description of fluid systems with molecular-based algebraic equations of state (EoSs) and by direct molecular simulation is common practice in chemical engineering and the physical sciences, but the two approaches are rarely closely coupled. The key for an integrated representation is through a well-defined force field and Hamiltonian at the molecular level. In developing coarse-grained intermolecular potential functions for the fluid state, one typically starts with a detailed, bottom-up quantum-mechanical or atomic-level description and then integrates out the unwanted degrees of freedom using a variety of techniques; an iterative heuristic simulation procedure is then used to refine the parameters of the model. By contrast, with a top-down technique, one can use an accurate EoS to link the macroscopic properties of the fluid and the force-field parameters. We discuss the latest developments in a top-down representation of fluids, with a particular focus on a group-contribution formulation of the statistical associating fluid theory (SAFT-γ). The accurate SAFT-γ EoS is used to estimate the parameters of the Mie force field, which can then be used with confidence in direct molecular simulations to obtain thermodynamic, structural, interfacial, and dynamical properties that are otherwise inaccessible from the EoS. This is exemplified for several prototypical fluids and mixtures, including carbon dioxide, hydrocarbons, perfluorohydrocarbons, and aqueous surfactants.

Local recovery of lithospheric stress tensor from GOCE gravitational tensor

NASA Astrophysics Data System (ADS)

Eshagh, Mehdi

2017-04-01

The sublithospheric stress due to mantle convection can be computed from gravity data and propagated through the lithosphere by solving the boundary-value problem of elasticity for the Earth's lithosphere. In this case, a full tensor of stress can be computed at any point inside this elastic layer. Here, we present mathematical foundations for recovering such a tensor from gravitational tensor measured at satellite altitudes. The mathematical relations will be much simpler in this way than the case of using gravity data as no derivative of spherical harmonics (SHs) or Legendre polynomials is involved in the expressions. Here, new relations between the SH coefficients of the stress and gravitational tensor elements are presented. Thereafter, integral equations are established from them to recover the elements of stress tensor from those of the gravitational tensor. The integrals have no closed-form kernels, but they are easy to invert and their spatial truncation errors are reducible. The integral equations are used to invert the real data of the gravity field and steady-state ocean circulation explorer mission (GOCE), in 2009 November, over the South American plate and its surroundings to recover the stress tensor at a depth of 35 km. The recovered stress fields are in good agreement with the tectonic and geological features of the area.

TOPICA/TORIC integration for self-consistent antenna and plasma analysis

NASA Astrophysics Data System (ADS)

Maggiora, Riccardo; Lancellotti, Vito; Milanesio, Daniele; Kyrytsya, Volodymyr; Vecchi, Giuseppe; Bonoli, Paul T.; Wright, John C.

2006-10-01

TOPICA [1] is a numerical suite conceived for prediction and analysis of plasma-facing antennas. It can handle real-life 3D antenna geometries (with housing, Faraday screen, etc.) as well as a realistic plasma model, including measured density and temperature profiles. TORIC [2] solves the finite Larmor radius wave equations in the ICRF regime in arbitrary axisymmetric toroidal plasmas. Due to the approach followed in developing TOPICA (i.e. the formal splitting of the problem in the vacuum region around the antenna and the plasma region inside the toroidal chamber), the code lends itself to handle toroidal plasmas, provided TORIC is run independently to yield the plasma surface admittance tensorsY (m,m',n). The latter enter directly into the integral equations solved by TOPICA, thus allowing a far more accurate plasma description that accounts for curvature effects. TOPICA outputs comprise, among others, the EM fields in front of the plasma: these can in turn be input to TORIC, in order to self-consistently determine the EM field propagation in the plasma. In this work, we report on the theory underlying the TOPICA/TORIC integration and the ongoing evolution of the two codes. [1] V. Lancellotti et al., Nucl. Fusion, 46 (2006) S476 [2] M. Brambilla, Plasma Phys. Contr. Fusion (1999) 41 1

Explicit solution of integrated 1 - exp equation for predicting accumulation and decline of concentrations for drugs obeying nonlinear saturation kinetics.

PubMed

Keller, Frieder; Hartmann, Bertram; Czock, David

2009-12-01

To describe nonlinear, saturable pharmacokinetics, the Michaelis-Menten equation is frequently used. However, the Michaelis-Menten equation has no integrated solution for concentrations but only for the time factor. Application of the Lambert W function was proposed recently to obtain an integrated solution of the Michaelis-Menten equation. As an alternative to the Michaelis-Menten equation, a 1 - exp equation has been used to describe saturable kinetics, with the advantage that the integrated 1 - exp equation has an explicit solution for concentrations. We used the integrated 1 - exp equation to predict the accumulation kinetics and the nonlinear concentration decline for a proposed fictive drug. In agreement with the recently proposed method, we found that for the integrated 1 - exp equation no steady state is obtained if the maximum rate of change in concentrations (Vmax) within interval (Tau) is less than the difference between peak and trough concentrations (Vmax x Tau < C peak - C trough).

Simulation of Jet Noise with OVERFLOW CFD Code and Kirchhoff Surface Integral

NASA Technical Reports Server (NTRS)

Kandula, M.; Caimi, R.; Voska, N. (Technical Monitor)

2002-01-01

An acoustic prediction capability for supersonic axisymmetric jets was developed on the basis of OVERFLOW Navier-Stokes CFD (Computational Fluid Dynamics) code of NASA Langley Research Center. Reynolds-averaged turbulent stresses in the flow field are modeled with the aid of Spalart-Allmaras one-equation turbulence model. Appropriate acoustic and outflow boundary conditions were implemented to compute time-dependent acoustic pressure in the nonlinear source-field. Based on the specification of acoustic pressure, its temporal and normal derivatives on the Kirchhoff surface, the near-field and the far-field sound pressure levels are computed via Kirchhoff surface integral, with the Kirchhoff surface chosen to enclose the nonlinear sound source region described by the CFD code. The methods are validated by a comparison of the predictions of sound pressure levels with the available data for an axisymmetric turbulent supersonic (Mach 2) perfectly expanded jet.

Simulation of Supersonic Jet Noise with the Adaptation of Overflow CFD Code and Kirchhoff Surface Integral

NASA Technical Reports Server (NTRS)

Kandula, Max; Caimi, Raoul; Steinrock, T. (Technical Monitor)

2001-01-01

An acoustic prediction capability for supersonic axisymmetric jets was developed on the basis of OVERFLOW Navier-Stokes CFD (Computational Fluid Dynamics) code of NASA Langley Research Center. Reynolds-averaged turbulent stresses in the flow field are modeled with the aid of Spalart-Allmaras one-equation turbulence model. Appropriate acoustic and outflow boundary conditions were implemented to compute time-dependent acoustic pressure in the nonlinear source-field. Based on the specification of acoustic pressure, its temporal and normal derivatives on the Kirchhoff surface, the near-field and the far-field sound pressure levels are computed via Kirchhoff surface integral, with the Kirchhoff surface chosen to enclose the nonlinear sound source region described by the CFD code. The methods are validated by a comparison of the predictions of sound pressure levels with the available data for an axisymmetric turbulent supersonic (Mach 2) perfectly expanded jet.

Chaos and nonlinear dynamics of single-particle orbits in a magnetotaillike magnetic field

NASA Technical Reports Server (NTRS)

Chen, J.; Palmadesso, P. J.

1986-01-01

The properties of charged-particle motion in Hamiltonian dynamics are studied in a magnetotaillike magnetic field configuration. It is shown by numerical integration of the equation of motion that the system is generally nonintegrable and that the particle motion can be classified into three distinct types of orbits: bounded integrable orbits, unbounded stochastic orbits, and unbounded transient orbits. It is also shown that different regions of the phase space exhibit qualitatively different responses to external influences. The concept of 'differential memory' in single-particle distributions is proposed. Physical implications for the dynamical properties of the magnetotail plasmas and the possible generation of non-Maxwellian features in the distribution functions are discussed.

Topics in structural dynamics: Nonlinear unsteady transonic flows and Monte Carlo methods in acoustics

NASA Technical Reports Server (NTRS)

Haviland, J. K.

1974-01-01

The results are reported of two unrelated studies. The first was an investigation of the formulation of the equations for non-uniform unsteady flows, by perturbation of an irrotational flow to obtain the linear Green's equation. The resulting integral equation was found to contain a kernel which could be expressed as the solution of the adjoint flow equation, a linear equation for small perturbations, but with non-constant coefficients determined by the steady flow conditions. It is believed that the non-uniform flow effects may prove important in transonic flutter, and that in such cases, the use of doublet type solutions of the wave equation would then prove to be erroneous. The second task covered an initial investigation into the use of the Monte Carlo method for solution of acoustical field problems. Computed results are given for a rectangular room problem, and for a problem involving a circular duct with a source located at the closed end.

Computer code for scattering from impedance bodies of revolution. Part 3: Surface impedance with s and phi variation. Analytical and numerical results

NASA Technical Reports Server (NTRS)

Uslenghi, Piergiorgio L. E.; Laxpati, Sharad R.; Kawalko, Stephen F.

1993-01-01

The third phase of the development of the computer codes for scattering by coated bodies that has been part of an ongoing effort in the Electromagnetics Laboratory of the Electrical Engineering and Computer Science Department at the University of Illinois at Chicago is described. The work reported discusses the analytical and numerical results for the scattering of an obliquely incident plane wave by impedance bodies of revolution with phi variation of the surface impedance. Integral equation formulation of the problem is considered. All three types of integral equations, electric field, magnetic field, and combined field, are considered. These equations are solved numerically via the method of moments with parametric elements. Both TE and TM polarization of the incident plane wave are considered. The surface impedance is allowed to vary along both the profile of the scatterer and in the phi direction. Computer code developed for this purpose determines the electric surface current as well as the bistatic radar cross section. The results obtained with this code were validated by comparing the results with available results for specific scatterers such as the perfectly conducting sphere. Results for the cone-sphere and cone-cylinder-sphere for the case of an axially incident plane were validated by comparing the results with the results with those obtained in the first phase of this project. Results for body of revolution scatterers with an abrupt change in the surface impedance along both the profile of the scatterer and the phi direction are presented.

Dissipative transport in superlattices within the Wigner function formalism

DOE PAGES

Jonasson, O.; Knezevic, I.

2015-07-30

Here, we employ the Wigner function formalism to simulate partially coherent, dissipative electron transport in biased semiconductor superlattices. We introduce a model collision integral with terms that describe energy dissipation, momentum relaxation, and the decay of spatial coherences (localization). Based on a particle-based solution to the Wigner transport equation with the model collision integral, we simulate quantum electronic transport at 10 K in a GaAs/AlGaAs superlattice and accurately reproduce its current density vs field characteristics obtained in experiment.

A Semi-Analytical Method for Determining the Energy Release Rate of Cracks in Adhesively-Bonded Single-Lap Composite Joints

NASA Technical Reports Server (NTRS)

Yang, Charles; Sun, Wenjun; Tomblin, John S.; Smeltzer, Stanley S., III

2007-01-01

A semi-analytical method for determining the strain energy release rate due to a prescribed interface crack in an adhesively-bonded, single-lap composite joint subjected to axial tension is presented. The field equations in terms of displacements within the joint are formulated by using first-order shear deformable, laminated plate theory together with kinematic relations and force equilibrium conditions. The stress distributions for the adherends and adhesive are determined after the appropriate boundary and loading conditions are applied and the equations for the field displacements are solved. Based on the adhesive stress distributions, the forces at the crack tip are obtained and the strain energy release rate of the crack is determined by using the virtual crack closure technique (VCCT). Additionally, the test specimen geometry from both the ASTM D3165 and D1002 test standards are utilized during the derivation of the field equations in order to correlate analytical models with future test results. The system of second-order differential field equations is solved to provide the adherend and adhesive stress response using the symbolic computation tool, Maple 9. Finite element analyses using J-integral as well as VCCT were performed to verify the developed analytical model. The finite element analyses were conducted using the commercial finite element analysis software ABAQUS. The results determined using the analytical method correlated well with the results from the finite element analyses.

A space-time tensor formulation for continuum mechanics in general curvilinear, moving, and deforming coordinate systems

NASA Technical Reports Server (NTRS)

Avis, L. M.

1976-01-01

Tensor methods are used to express the continuum equations of motion in general curvilinear, moving, and deforming coordinate systems. The space-time tensor formulation is applicable to situations in which, for example, the boundaries move and deform. Placing a coordinate surface on such a boundary simplifies the boundary condition treatment. The space-time tensor formulation is also applicable to coordinate systems with coordinate surfaces defined as surfaces of constant pressure, density, temperature, or any other scalar continuum field function. The vanishing of the function gradient components along the coordinate surfaces may simplify the set of governing equations. In numerical integration of the equations of motion, the freedom of motion of the coordinate surfaces provides a potential for enhanced resolution of the continuum field function. An example problem of an incompressible, inviscid fluid with a top free surface is considered, where the surfaces of constant pressure (including the top free surface) are coordinate surfaces.

Vibration of initially stressed carbon nanotubes under magneto-thermal environment for nanoparticle delivery via higher-order nonlocal strain gradient theory

NASA Astrophysics Data System (ADS)

Farajpour, M. R.; Shahidi, A. R.; Tabataba'i-Nasab, F.; Farajpour, A.

2018-06-01

In this paper, the forced vibration of a single-walled carbon nanotube (SWCNT) under a moving nanoparticle is investigated based on the higher-order nonlocal strain gradient theory. The SWCNT is subjected to thermo-mechanical stresses and an external longitudinal magnetic field. The influences of higher-order stress gradients in conjunction with the strain gradient nonlocality are taken into account. Using Hamilton's principle and Maxwell's equations, the higher-order differential equations of motion are derived. An analytical solution is obtained for the dynamic deflection of SWCNTs using the Galerkin method. Furthermore, the governing differential equation is solved numerically using the precise integration method. The results of the two solution procedures are compared and an excellent agreement is found between them. Finally, the influences of various scale parameters, the velocity of the moving nanoparticle, the initial axial stress, the temperature change and longitudinal magnetic field on the dynamic response of SWCNTs are investigated.

Identification of Spurious Signals from Permeable Ffowcs Williams and Hawkings Surfaces

NASA Technical Reports Server (NTRS)

Lopes, Leonard V.; Boyd, David D., Jr.; Nark, Douglas M.; Wiedemann, Karl E.

2017-01-01

Integral forms of the permeable surface formulation of the Ffowcs Williams and Hawkings (FW-H) equation often require an input in the form of a near field Computational Fluid Dynamics (CFD) solution to predict noise in the near or far field from various types of geometries. The FW-H equation involves three source terms; two surface terms (monopole and dipole) and a volume term (quadrupole). Many solutions to the FW-H equation, such as several of Farassat's formulations, neglect the quadrupole term. Neglecting the quadrupole term in permeable surface formulations leads to inaccuracies called spurious signals. This paper explores the concept of spurious signals, explains how they are generated by specifying the acoustic and hydrodynamic surface properties individually, and provides methods to determine their presence, regardless of whether a correction algorithm is employed. A potential approach based on the equivalent sources method (ESM) and the sensitivity of Formulation 1A (Formulation S1A) is also discussed for the removal of spurious signals.

{lambda} elements for singular problems in CFD: Viscoelastic fluids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wong, K.K.; Surana, K.S.

1996-10-01

This paper presents two dimensional {lambda} element formulation for viscoelastic fluid flow containing point singularities in the flow field. The flow of viscoelastic fluid even without singularities are a difficult class of problems for increasing Deborah number or Weissenburg number due to increased dominance of convective terms and thus increased hyperbolicity. In the present work the equations of fluid motion and the constitutive laws are recast in the form of a first order system of coupled equations with the use of auxiliary variables. The velocity, pressure and stresses are interpolated using equal order C{sup 0} {lambda} element approximations. The Leastmore » Squares Finite Element Method (LSFEM) is used to construct the integral form (error functional I) corresponding to these equations. The error functional is constructed by taking the integrated sum of the squares of the errors or residuals (over the whole discretization) resulting when the element approximation is substituted into these equations. The conditions resulting from the minimization of the error functional are satisfied by using Newton`s method with line search. LSFEM has much superior performance when dealing with non-linear and convection dominated problems.« less

Scattering of electromagnetic plane wave from a perfect electric conducting strip placed at interface of topological insulator-chiral medium

NASA Astrophysics Data System (ADS)

Shoukat, Sobia; Naqvi, Qaisar A.

2016-12-01

In this manuscript, scattering from a perfect electric conducting strip located at planar interface of topological insulator (TI)-chiral medium is investigated using the Kobayashi Potential method. Longitudinal components of electric and magnetic vector potential in terms of unknown weighting function are considered. Use of related set of boundary conditions yields two algebraic equations and four dual integral equations (DIEs). Integrand of two DIEs are expanded in terms of the characteristic functions with expansion coefficients which must satisfy, simultaneously, the discontinuous property of the Weber-Schafheitlin integrals, required edge and boundary conditions. The resulting expressions are then combined with algebraic equations to express the weighting function in terms of expansion coefficients, these expansion coefficients are then substituted in remaining DIEs. The projection is applied using the Jacobi polynomials. This treatment yields matrix equation for expansion coefficients which is solved numerically. These unknown expansion coefficients are used to find the scattered field. The far zone scattering width is investigated with respect to different parameters of the geometry, i.e, chirality of chiral medium, angle of incidence, size of the strip. Significant effects of different parameters including TI parameter on the scattering width are noted.

An evaluation of three two-dimensional computational fluid dynamics codes including low Reynolds numbers and transonic Mach numbers

NASA Technical Reports Server (NTRS)

Hicks, Raymond M.; Cliff, Susan E.

1991-01-01

Full-potential, Euler, and Navier-Stokes computational fluid dynamics (CFD) codes were evaluated for use in analyzing the flow field about airfoils sections operating at Mach numbers from 0.20 to 0.60 and Reynolds numbers from 500,000 to 2,000,000. The potential code (LBAUER) includes weakly coupled integral boundary layer equations for laminar and turbulent flow with simple transition and separation models. The Navier-Stokes code (ARC2D) uses the thin-layer formulation of the Reynolds-averaged equations with an algebraic turbulence model. The Euler code (ISES) includes strongly coupled integral boundary layer equations and advanced transition and separation calculations with the capability to model laminar separation bubbles and limited zones of turbulent separation. The best experiment/CFD correlation was obtained with the Euler code because its boundary layer equations model the physics of the flow better than the other two codes. An unusual reversal of boundary layer separation with increasing angle of attack, following initial shock formation on the upper surface of the airfoil, was found in the experiment data. This phenomenon was not predicted by the CFD codes evaluated.

Permeable Surface Corrections for Ffowcs Williams and Hawkings Integrals

NASA Technical Reports Server (NTRS)

Lockard, David P.; Casper, Jay H.

2005-01-01

The acoustic prediction methodology discussed herein applies an acoustic analogy to calculate the sound generated by sources in an aerodynamic simulation. Sound is propagated from the computed flow field by integrating the Ffowcs Williams and Hawkings equation on a suitable control surface. Previous research suggests that, for some applications, the integration surface must be placed away from the solid surface to incorporate source contributions from within the flow volume. As such, the fluid mechanisms in the input flow field that contribute to the far-field noise are accounted for by their mathematical projection as a distribution of source terms on a permeable surface. The passage of nonacoustic disturbances through such an integration surface can result in significant error in an acoustic calculation. A correction for the error is derived in the frequency domain using a frozen gust assumption. The correction is found to work reasonably well in several test cases where the error is a small fraction of the actual radiated noise. However, satisfactory agreement has not been obtained between noise predictions using the solution from a three-dimensional, detached-eddy simulation of flow over a cylinder.

Numerical inverse method predicting acoustic spinning modes radiated by a ducted fan from free-field test data.

PubMed

Lewy, Serge

2008-07-01

Spinning modes generated by a ducted turbofan at a given frequency determine the acoustic free-field directivity. An inverse method starting from measured directivity patterns is interesting in providing information on the noise sources without requiring tedious spinning-mode experimental analyses. According to a previous article, equations are based on analytical modal splitting inside a cylindrical duct and on a Rayleigh or a Kirchhoff integral on the duct exit cross section to get far-field directivity. Equations are equal in number to free-field measurement locations and the unknowns are the propagating mode amplitudes (there are generally more unknowns than equations). A MATLAB procedure has been implemented by using either the pseudoinverse function or the backslash operator. A constraint comes from the fact that squared modal amplitudes must be positive which involves an iterative least squares fitting. Numerical simulations are discussed along with several examples based on tests performed by Rolls-Royce in the framework of a European project. It is assessed that computation is very fast and it well fits the measured directivities, but the solution depends on the method and is not unique. This means that the initial set of modes should be chosen according to any known physical property of the acoustic sources.

Double Alfvén waves

NASA Astrophysics Data System (ADS)

Webb, G. M.; Hu, Q.; Dasgupta, B.; Zank, G. P.

2012-02-01

Double Alfvén wave solutions of the magnetohydrodynamic equations in which the physical variables (the gas density ρ, fluid velocity u, gas pressure p, and magnetic field induction B) depend only on two independent wave phases ϕ1(x,t) and ϕ2(x,t) are obtained. The integrals for the double Alfvén wave are the same as for simple waves, namely, the gas pressure, magnetic pressure, and group velocity of the wave are constant. Compatibility conditions on the evolution of the magnetic field B due to changes in ϕ1 and ϕ2, as well as constraints due to Gauss's law ∇ · B = 0 are discussed. The magnetic field lines and hodographs of B in which the tip of the magnetic field B moves on the sphere |B| = B = const. are used to delineate the physical characteristics of the wave. Hamilton's equations for the simple Alfvén wave with wave normal n(ϕ), and with magnetic induction B(ϕ) in which ϕ is the wave phase, are obtained by using the Frenet-Serret equations for curves x=X(ϕ) in differential geometry. The use of differential geometry of 2D surfaces in a 3D Euclidean space to describe double Alfvén waves is briefly discussed.

Calculation of unsteady transonic flows with mild separation by viscous-inviscid interaction

NASA Technical Reports Server (NTRS)

Howlett, James T.

1992-01-01

This paper presents a method for calculating viscous effects in two- and three-dimensional unsteady transonic flow fields. An integral boundary-layer method for turbulent viscous flow is coupled with the transonic small-disturbance potential equation in a quasi-steady manner. The viscous effects are modeled with Green's lag-entrainment equations for attached flow and an inverse boundary-layer method for flows that involve mild separation. The boundary-layer method is used stripwise to approximate three-dimensional effects. Applications are given for two-dimensional airfoils, aileron buzz, and a wing planform. Comparisons with inviscid calculations, other viscous calculation methods, and experimental data are presented. The results demonstrate that the present technique can economically and accurately calculate unsteady transonic flow fields that have viscous-inviscid interactions with mild flow separation.

Solving the Hamilton-Jacobi equation for general relativity

NASA Astrophysics Data System (ADS)

Parry, J.; Salopek, D. S.; Stewart, J. M.

1994-03-01

We demonstrate a systematic method for solving the Hamilton-Jacobi equation for general relativity with the inclusion of matter fields. The generating functional is expanded in a series of spatial gradients. Each term is manifestly invariant under reparametrizations of the spatial coordinates (``gauge invariant''). At each order we solve the Hamiltonian constraint using a conformal transformation of the three-metric as well as a line integral in superspace. This gives a recursion relation for the generating functional which then may be solved to arbitrary order simply by functionally differentiating previous orders. At fourth order in spatial gradients we demonstrate solutions for irrotational dust as well as for a scalar field. We explicitly evolve the three-metric to the same order. This method can be used to derive the Zel'dovich approximation for general relativity.

The effects of pressure anisotropy on Birkeland currents in dipole and stretched magnetospheres

NASA Technical Reports Server (NTRS)

Birmingham, Thomas J.

1992-01-01

Attention is given to two effects which modify the rate of generation of Birkeland currents from the values given by the Vasyliunas (1970) formula in a dipole, namely, nonisotropic plasma pressure and the radial distention of magnetic field lines. The parallel current at any given point is the integrated effect of the diversion of perpendicular currents along the length of the flux tube from the equator. The result for j-parallel in I is fully nonlinear. In a dipole field the effect of anisotropy is modest: j-parallel at the ionosphere is, irrespective of the r0 value, about factor of 2.4 larger for a large P-parallel anisotropy (r = 0.1) than for the isotropic case and factor of 0.2 smaller for r = 10. In the stretched field the comparable values are factor of 10 and factor of 0.06 for a field line intersecting the ionosphere at a dipole colatitude of 16.4 deg and crossing the equator at r0 of 20. The results exhibit differences in plasma density and plasma pressure along field lines between the stretched and dipole models.

Unique topological characterization of braided magnetic fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yeates, A. R.; Hornig, G.

We introduce a topological flux function to quantify the topology of magnetic braids: non-zero, line-tied magnetic fields whose field lines all connect between two boundaries. This scalar function is an ideal invariant defined on a cross-section of the magnetic field, and measures the average poloidal magnetic flux around any given field line, or the average pairwise crossing number between a given field line and all others. Moreover, its integral over the cross-section yields the relative magnetic helicity. Using the fact that the flux function is also an action in the Hamiltonian formulation of the field line equations, we prove thatmore » it uniquely characterizes the field line mapping and hence the magnetic topology.« less

Dressing the post-Newtonian two-body problem and classical effective field theory

NASA Astrophysics Data System (ADS)

Kol, Barak; Smolkin, Michael

2009-12-01

We apply a dressed perturbation theory to better organize and economize the computation of high orders of the 2-body effective action of an inspiralling post-Newtonian (PN) gravitating binary. We use the effective field theory approach with the nonrelativistic field decomposition (NRG fields). For that purpose we develop quite generally the dressing theory of a nonlinear classical field theory coupled to pointlike sources. We introduce dressed charges and propagators, but unlike the quantum theory there are no dressed bulk vertices. The dressed quantities are found to obey recursive integral equations which succinctly encode parts of the diagrammatic expansion, and are the classical version of the Schwinger-Dyson equations. Actually, the classical equations are somewhat stronger since they involve only finitely many quantities, unlike the quantum theory. Classical diagrams are shown to factorize exactly when they contain nonlinear worldline vertices, and we classify all the possible topologies of irreducible diagrams for low loop numbers. We apply the dressing program to our post-Newtonian case of interest. The dressed charges consist of the dressed energy-momentum tensor after a nonrelativistic decomposition, and we compute all dressed charges (in the harmonic gauge) appearing up to 2PN in the 2-body effective action (and more). We determine the irreducible skeleton diagrams up to 3PN and we employ the dressed charges to compute several terms beyond 2PN.

Acoustic plane wave diffraction from a truncated semi-infinite cone in axial irradiation

NASA Astrophysics Data System (ADS)

Kuryliak, Dozyslav; Lysechko, Victor

2017-11-01

The diffraction problem of the plane acoustic wave on the semi-infinite truncated soft and rigid cones in the case of axial incidence is solved. The problem is formulated as a boundary-value problem in terms of Helmholtz equation, with Dirichlet and Neumann boundary conditions, for scattered velocity potential. The incident field is taken to be the total field of semi-infinite cone, the expression of which is obtained by solving the auxiliary diffraction problem by the use of Kontorovich-Lebedev integral transformation. The diffracted field is sought via the expansion in series of the eigenfunctions for subdomains of the Helmholtz equation taking into account the edge condition. The corresponding diffraction problem is reduced to infinite system of linear algebraic equations (ISLAE) making use of mode matching technique and orthogonality properties of the Legendre functions. The method of analytical regularization is applied in order to extract the singular part in ISLAE, invert it exactly and reduce the problem to ISLAE of the second kind, which is readily amenable to calculation. The numerical solution of this system relies on the reduction method; and its accuracy depends on the truncation order. The case of degeneration of the truncated semi-infinite cone into an aperture in infinite plane is considered. Characteristic features of diffracted field in near and far fields as functions of cone's parameters are examined.

Signs and stability in higher-derivative gravity

NASA Astrophysics Data System (ADS)

Narain, Gaurav

2018-02-01

Perturbatively renormalizable higher-derivative gravity in four space-time dimensions with arbitrary signs of couplings has been considered. Systematic analysis of the action with arbitrary signs of couplings in Lorentzian flat space-time for no-tachyons, fixes the signs. Feynman + i𝜖 prescription for these signs further grants necessary convergence in path-integral, suppressing the field modes with large action. This also leads to a sensible wick rotation where quantum computation can be performed. Running couplings for these sign of parameters make the massive tensor ghost innocuous leading to a stable and ghost-free renormalizable theory in four space-time dimensions. The theory has a transition point arising from renormalization group (RG) equations, where the coefficient of R2 diverges without affecting the perturbative quantum field theory (QFT). Redefining this coefficient gives a better handle over the theory around the transition point. The flow equations push the flow of parameters across the transition point. The flow beyond the transition point is analyzed using the one-loop RG equations which shows that the regime beyond the transition point has unphysical properties: there are tachyons, the path-integral loses positive definiteness, Newton’s constant G becomes negative and large, and perturbative parameters become large. These shortcomings indicate a lack of completeness beyond the transition point and need of a nonperturbative treatment of the theory beyond the transition point.

First independent lunar gravity field solution in the framework of project GRAZIL

NASA Astrophysics Data System (ADS)

Wirnsberger, Harald; Krauss, Sandro; Klinger, Beate; Mayer-Gürr, Torsten

2017-04-01

The twin satellite mission Gravity Recovery and Interior Laboratory (GRAIL) aims to recovering the lunar gravity field by means of intersatellite Ka-band ranging (KBR) observations. In order to exploit the potential of KBR data, absolute position information of the two probes is required. Hitherto, the Graz lunar gravity field models (GrazLGM) relies on the official orbit products provided by NASA. In this contribution, we present for the first time a completely independent Graz lunar gravity field model to spherical harmonic degree and order 420. The reduced dynamic orbits of the two probes are determined using variational equations following a batch least squares differential adjustment process. These orbits are based on S-band radiometric tracking data collected by the Deep Space Network and are used for the independent GRAIL gravity field recovery. To reveal a highly accurate lunar gravity field, an integral equation approach using short orbital arcs is adopted to process the KBR data. A comparison to state-of-the-art lunar gravity models computed at NASA-GSFC, NASA-JPL and AIUB demonstrate the progress of Graz lunar gravity field models derived within the project GRAZIL.

On the instability of wave-fields with JONSWAP spectra to inhomogeneous disturbances, and the consequent long-time evolution

NASA Astrophysics Data System (ADS)

Ribal, A.; Stiassnie, M.; Babanin, A.; Young, I.

2012-04-01

The instability of two-dimensional wave-fields and its subsequent evolution in time are studied by means of the Alber equation for narrow-banded random surface-waves in deep water subject to inhomogeneous disturbances. A linear partial differential equation (PDE) is obtained after applying an inhomogeneous disturbance to the Alber's equation and based on the solution of this PDE, the instability of the ocean wave surface is studied for a JONSWAP spectrum, which is a realistic ocean spectrum with variable directional spreading and steepness. The steepness of the JONSWAP spectrum depends on γ and α which are the peak-enhancement factor and energy scale of the spectrum respectively and it is found that instability depends on the directional spreading, α and γ. Specifically, if the instability stops due to the directional spreading, increase of the steepness by increasing α or γ can reactivate it. This result is in qualitative agreement with the recent large-scale experiment and new theoretical results. In the instability area of α-γ plane, a long-time evolution has been simulated by integrating Alber's equation numerically and recurrent evolution is obtained which is the stochastic counterpart of the Fermi-Pasta-Ulam recurrence obtained for the cubic Schrödinger equation.

High-order boundary integral equation solution of high frequency wave scattering from obstacles in an unbounded linearly stratified medium

NASA Astrophysics Data System (ADS)

Barnett, Alex H.; Nelson, Bradley J.; Mahoney, J. Matthew

2015-09-01

We apply boundary integral equations for the first time to the two-dimensional scattering of time-harmonic waves from a smooth obstacle embedded in a continuously-graded unbounded medium. In the case we solve, the square of the wavenumber (refractive index) varies linearly in one coordinate, i.e. (Δ + E +x2) u (x1 ,x2) = 0 where E is a constant; this models quantum particles of fixed energy in a uniform gravitational field, and has broader applications to stratified media in acoustics, optics and seismology. We evaluate the fundamental solution efficiently with exponential accuracy via numerical saddle-point integration, using the truncated trapezoid rule with typically 102 nodes, with an effort that is independent of the frequency parameter E. By combining with a high-order Nyström quadrature, we are able to solve the scattering from obstacles 50 wavelengths across to 11 digits of accuracy in under a minute on a desktop or laptop.

A piece of cake: the ground-state energies in γ i -deformed = 4 SYM theory at leading wrapping order

NASA Astrophysics Data System (ADS)

Fokken, Jan; Sieg, Christoph; Wilhelm, Matthias

2014-09-01

In the non-supersymmetric γi-deformed = 4 SYM theory, the scaling dimensions of the operators tr[ Z L ] composed of L scalar fields Z receive finite-size wrapping and prewrapping corrections in the 't Hooft limit. In this paper, we calculate these scaling dimensions to leading wrapping order directly from Feynman diagrams. For L ≥ 3, the result is proportional to the maximally transcendental `cake' integral. It matches with an earlier result obtained from the integrability-based Lüscher corrections, TBA and Y-system equations. At L = 2, where the integrability-based equations yield infinity, we find a finite rational result. This result is renormalization-scheme dependent due to the non-vanishing β-function of an induced quartic scalar double-trace coupling, on which we have reported earlier. This explicitly shows that conformal invariance is broken — even in the 't Hooft limit. [Figure not available: see fulltext.

Exact analytical formulae for linearly distributed vortex and source sheets in uence computation in 2D vortex methods

NASA Astrophysics Data System (ADS)

Kuzmina, K. S.; Marchevsky, I. K.; Ryatina, E. P.

2017-11-01

We consider the methodology of numerical schemes development for two-dimensional vortex method. We describe two different approaches to deriving integral equation for unknown vortex sheet intensity. We simulate the velocity of the surface line of an airfoil as the influence of attached vortex and source sheets. We consider a polygonal approximation of the airfoil and assume intensity distributions of free and attached vortex sheets and attached source sheet to be approximated with piecewise constant or piecewise linear (continuous or discontinuous) functions. We describe several specific numerical schemes that provide different accuracy and have a different computational cost. The study shows that a Galerkin-type approach to solving boundary integral equation requires computing several integrals and double integrals over the panels. We obtain exact analytical formulae for all the necessary integrals, which makes it possible to raise significantly the accuracy of vortex sheet intensity computation and improve the quality of velocity and vorticity field representation, especially in proximity to the surface line of the airfoil. All the formulae are written down in the invariant form and depend only on the geometric relationship between the positions of the beginnings and ends of the panels.

Development of Multistep and Degenerate Variational Integrators for Applications in Plasma Physics

NASA Astrophysics Data System (ADS)

Ellison, Charles Leland

Geometric integrators yield high-fidelity numerical results by retaining conservation laws in the time advance. A particularly powerful class of geometric integrators is symplectic integrators, which are widely used in orbital mechanics and accelerator physics. An important application presently lacking symplectic integrators is the guiding center motion of magnetized particles represented by non-canonical coordinates. Because guiding center trajectories are foundational to many simulations of magnetically confined plasmas, geometric guiding center algorithms have high potential for impact. The motivation is compounded by the need to simulate long-pulse fusion devices, including ITER, and opportunities in high performance computing, including the use of petascale resources and beyond. This dissertation uses a systematic procedure for constructing geometric integrators --- known as variational integration --- to deliver new algorithms for guiding center trajectories and other plasma-relevant dynamical systems. These variational integrators are non-trivial because the Lagrangians of interest are degenerate - the Euler-Lagrange equations are first-order differential equations and the Legendre transform is not invertible. The first contribution of this dissertation is that variational integrators for degenerate Lagrangian systems are typically multistep methods. Multistep methods admit parasitic mode instabilities that can ruin the numerical results. These instabilities motivate the second major contribution: degenerate variational integrators. By replicating the degeneracy of the continuous system, degenerate variational integrators avoid parasitic mode instabilities. The new methods are therefore robust geometric integrators for degenerate Lagrangian systems. These developments in variational integration theory culminate in one-step degenerate variational integrators for non-canonical magnetic field line flow and guiding center dynamics. The guiding center integrator assumes coordinates such that one component of the magnetic field is zero; it is shown how to construct such coordinates for nested magnetic surface configurations. Additionally, collisional drag effects are incorporated in the variational guiding center algorithm for the first time, allowing simulation of energetic particle thermalization. Advantages relative to existing canonical-symplectic and non-geometric algorithms are numerically demonstrated. All algorithms have been implemented as part of a modern, parallel, ODE-solving library, suitable for use in high-performance simulations.

Mean-field equations for neuronal networks with arbitrary degree distributions.

PubMed

Nykamp, Duane Q; Friedman, Daniel; Shaker, Sammy; Shinn, Maxwell; Vella, Michael; Compte, Albert; Roxin, Alex

2017-04-01

The emergent dynamics in networks of recurrently coupled spiking neurons depends on the interplay between single-cell dynamics and network topology. Most theoretical studies on network dynamics have assumed simple topologies, such as connections that are made randomly and independently with a fixed probability (Erdös-Rényi network) (ER) or all-to-all connected networks. However, recent findings from slice experiments suggest that the actual patterns of connectivity between cortical neurons are more structured than in the ER random network. Here we explore how introducing additional higher-order statistical structure into the connectivity can affect the dynamics in neuronal networks. Specifically, we consider networks in which the number of presynaptic and postsynaptic contacts for each neuron, the degrees, are drawn from a joint degree distribution. We derive mean-field equations for a single population of homogeneous neurons and for a network of excitatory and inhibitory neurons, where the neurons can have arbitrary degree distributions. Through analysis of the mean-field equations and simulation of networks of integrate-and-fire neurons, we show that such networks have potentially much richer dynamics than an equivalent ER network. Finally, we relate the degree distributions to so-called cortical motifs.

Mean-field equations for neuronal networks with arbitrary degree distributions

NASA Astrophysics Data System (ADS)

Nykamp, Duane Q.; Friedman, Daniel; Shaker, Sammy; Shinn, Maxwell; Vella, Michael; Compte, Albert; Roxin, Alex

2017-04-01

The emergent dynamics in networks of recurrently coupled spiking neurons depends on the interplay between single-cell dynamics and network topology. Most theoretical studies on network dynamics have assumed simple topologies, such as connections that are made randomly and independently with a fixed probability (Erdös-Rényi network) (ER) or all-to-all connected networks. However, recent findings from slice experiments suggest that the actual patterns of connectivity between cortical neurons are more structured than in the ER random network. Here we explore how introducing additional higher-order statistical structure into the connectivity can affect the dynamics in neuronal networks. Specifically, we consider networks in which the number of presynaptic and postsynaptic contacts for each neuron, the degrees, are drawn from a joint degree distribution. We derive mean-field equations for a single population of homogeneous neurons and for a network of excitatory and inhibitory neurons, where the neurons can have arbitrary degree distributions. Through analysis of the mean-field equations and simulation of networks of integrate-and-fire neurons, we show that such networks have potentially much richer dynamics than an equivalent ER network. Finally, we relate the degree distributions to so-called cortical motifs.

Mathematical analysis of thermal diffusion shock waves

NASA Astrophysics Data System (ADS)

Gusev, Vitalyi; Craig, Walter; Livoti, Roberto; Danworaphong, Sorasak; Diebold, Gerald J.

2005-10-01

Thermal diffusion, also known as the Ludwig-Soret effect, refers to the separation of mixtures in a temperature gradient. For a binary mixture the time dependence of the change in concentration of each species is governed by a nonlinear partial differential equation in space and time. Here, an exact solution of the Ludwig-Soret equation without mass diffusion for a sinusoidal temperature field is given. The solution shows that counterpropagating shock waves are produced which slow and eventually come to a halt. Expressions are found for the shock time for two limiting values of the starting density fraction. The effects of diffusion on the development of the concentration profile in time and space are found by numerical integration of the nonlinear differential equation.

Numerical Solution of the Gyrokinetic Poisson Equation in TEMPEST

NASA Astrophysics Data System (ADS)

Dorr, Milo; Cohen, Bruce; Cohen, Ronald; Dimits, Andris; Hittinger, Jeffrey; Kerbel, Gary; Nevins, William; Rognlien, Thomas; Umansky, Maxim; Xiong, Andrew; Xu, Xueqiao

2006-10-01

The gyrokinetic Poisson (GKP) model in the TEMPEST continuum gyrokinetic edge plasma code yields the electrostatic potential due to the charge density of electrons and an arbitrary number of ion species including the effects of gyroaveraging in the limit kρ1. The TEMPEST equations are integrated as a differential algebraic system involving a nonlinear system solve via Newton-Krylov iteration. The GKP preconditioner block is inverted using a multigrid preconditioned conjugate gradient (CG) algorithm. Electrons are treated as kinetic or adiabatic. The Boltzmann relation in the adiabatic option employs flux surface averaging to maintain neutrality within field lines and is solved self-consistently with the GKP equation. A decomposition procedure circumvents the near singularity of the GKP Jacobian block that otherwise degrades CG convergence.

Electromagnetic beam diffraction by a finite lamellar structure: an aperiodic coupled-wave method.

PubMed

Guizal, Brahim; Barchiesi, Dominique; Felbacq, Didier

2003-12-01

We have developed a new formulation of the coupled-wave method (CWM) to handle aperiodic lamellar structures, and it will be referred to as the aperiodic coupled-wave method (ACWM). The space is still divided into three regions, but the fields are written by use of their Fourier integrals instead of the Fourier series. In the modulated region the relative permittivity is represented by its Fourier transform, and then a set of integro-differential equations is derived. Discretizing the last system leads to a set of ordinary differential equations that is reduced to an eigenvalue problem, as is usually done in the CWM. To assess the method, we compare our results with three independent formalisms: the Rayleigh perturbation method for small samples, the volume integral method, and the finite-element method.

Quantum electron levels in the field of a charged black hole

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dokuchaev, V. I.; Eroshenko, Yu. N., E-mail: eroshenko@ms2.inr.ac.ru

2015-12-15

Stationary solutions of the Dirac equation in the metric of the charged Reissner–Nordstrom black hole are found. In the case of an extremal black hole, the normalization integral of the wave functions is finite, and the regular stationary solution is physically self-consistent. The presence of quantum electron levels under the Cauchy horizon can have an impact on the final stage of the Hawking evaporation of the black hole, as well as on the particle scattering in the field of the black hole.

Electron kinematics in a plasma focus

NASA Technical Reports Server (NTRS)

Hohl, F.; Gary, S. P.

1977-01-01

The results of numerical integrations of the three-dimensional relativistic equations of motion of electrons subject to given electric and magnetic fields are presented. Fields due to two different models are studied: (1) a circular distribution of current filaments, and (2) a uniform current distribution; both the collapse and the current reduction phases are studied in each model. Decreasing current in the uniform current model yields 100 keV electrons accelerated toward the anode and, as for earlier ion computations, provides general agreement with experimental results.

Propagation of waves from an arbitrary shaped surface-A generalization of the Fresnel diffraction integral

NASA Astrophysics Data System (ADS)

Feshchenko, R. M.; Vinogradov, A. V.; Artyukov, I. A.

2018-04-01

Using the method of Laplace transform the field amplitude in the paraxial approximation is found in the two-dimensional free space using initial values of the amplitude specified on an arbitrary shaped monotonic curve. The obtained amplitude depends on one a priori unknown function, which can be found from a Volterra first kind integral equation. In a special case of field amplitude specified on a concave parabolic curve the exact solution is derived. Both solutions can be used to study the light propagation from arbitrary surfaces including grazing incidence X-ray mirrors. They can find applications in the analysis of coherent imaging problems of X-ray optics, in phase retrieval algorithms as well as in inverse problems in the cases when the initial field amplitude is sought on a curved surface.

A rapid boundary integral equation technique for protein electrostatics

NASA Astrophysics Data System (ADS)

Grandison, Scott; Penfold, Robert; Vanden-Broeck, Jean-Marc

2007-06-01

A new boundary integral formulation is proposed for the solution of electrostatic field problems involving piecewise uniform dielectric continua. Direct Coulomb contributions to the total potential are treated exactly and Green's theorem is applied only to the residual reaction field generated by surface polarisation charge induced at dielectric boundaries. The implementation shows significantly improved numerical stability over alternative schemes involving the total field or its surface normal derivatives. Although strictly respecting the electrostatic boundary conditions, the partitioned scheme does introduce a jump artefact at the interface. Comparison against analytic results in canonical geometries, however, demonstrates that simple interpolation near the boundary is a cheap and effective way to circumvent this characteristic in typical applications. The new scheme is tested in a naive model to successfully predict the ground state orientation of biomolecular aggregates comprising the soybean storage protein, glycinin.

A general time-dependent stochastic method for solving Parker's transport equation in spherical coordinates

NASA Astrophysics Data System (ADS)

Pei, C.; Bieber, J. W.; Burger, R. A.; Clem, J.

2010-12-01

We present a detailed description of our newly developed stochastic approach for solving Parker's transport equation, which we believe is the first attempt to solve it with time dependence in 3-D, evolving from our 3-D steady state stochastic approach. Our formulation of this method is general and is valid for any type of heliospheric magnetic field, although we choose the standard Parker field as an example to illustrate the steps to calculate the transport of galactic cosmic rays. Our 3-D stochastic method is different from other stochastic approaches in the literature in several ways. For example, we employ spherical coordinates to integrate directly, which makes the code much more efficient by reducing coordinate transformations. What is more, the equivalence between our stochastic differential equations and Parker's transport equation is guaranteed by Ito's theorem in contrast to some other approaches. We generalize the technique for calculating particle flux based on the pseudoparticle trajectories for steady state solutions and for time-dependent solutions in 3-D. To validate our code, first we show that good agreement exists between solutions obtained by our steady state stochastic method and a traditional finite difference method. Then we show that good agreement also exists for our time-dependent method for an idealized and simplified heliosphere which has a Parker magnetic field and a simple initial condition for two different inner boundary conditions.

Finite-Strain Fractional-Order Viscoelastic (FOV) Material Models and Numerical Methods for Solving Them

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Diethelm, Kai; Gray, Hugh R. (Technical Monitor)

2002-01-01

Fraction-order viscoelastic (FOV) material models have been proposed and studied in 1D since the 1930's, and were extended into three dimensions in the 1970's under the assumption of infinitesimal straining. It was not until 1997 that Drozdov introduced the first finite-strain FOV constitutive equations. In our presentation, we shall continue in this tradition by extending the standard, FOV, fluid and solid, material models introduced in 1971 by Caputo and Mainardi into 3D constitutive formula applicable for finite-strain analyses. To achieve this, we generalize both the convected and co-rotational derivatives of tensor fields to fractional order. This is accomplished by defining them first as body tensor fields and then mapping them into space as objective Cartesian tensor fields. Constitutive equations are constructed using both variants for fractional rate, and their responses are contrasted in simple shear. After five years of research and development, we now possess a basic suite of numerical tools necessary to study finite-strain FOV constitutive equations and their iterative refinement into a mature collection of material models. Numerical methods still need to be developed for efficiently solving fraction al-order integrals, derivatives, and differential equations in a finite element setting where such constitutive formulae would need to be solved at each Gauss point in each element of a finite model, which can number into the millions in today's analysis.

Development and application of discontinuous Galerkin method for the solution of two-dimensional Maxwell equations

NASA Astrophysics Data System (ADS)

Wong, See-Cheuk

We inhabit an environment of electromagnetic (EM) waves. The waves within the EM spectrum---whether light, radio, or microwaves---all obey the same physical laws. A band in the spectrum is designated to the microwave frequencies (30MHz--300GHz), at which radar systems operate. The precise modeling of the scattered EM-ields about a target, as well as the numerical prediction of the radar return is the crux of the computational electromagnetics (CEM) problems. The signature or return from a target observed by radar is commonly provided in the form of radar cross section (RCS). Incidentally, the efforts in the reduction of such return forms the basis of stealth aircraft design. The object of this dissertation is to extend Discontinuous Galerkin (DG) method to solve numerically the Maxwell equations for scatterings from perfect electric conductor (PEC) objects. The governing equations are derived by writing the Maxwell equations in conservation-law form for scattered field quantities. The transverse magnetic (TM) and the transverse electric (TE) waveforms of the Maxwell equations are considered. A finite-element scheme is developed with proper representations for the electric and magnetic fluxes at a cell interface to account for variations in properties, in both space and time. A characteristic sub-path integration process, known as the "Riemann solver" is involved. An explicit Runge-Kutta Discontinuous Galerkin (RKDG) upwind scheme, which is fourth-order accurate in time and second-order in space, is employed to solve the TM and TE equations. Arbitrary cross-sectioned bodies are modeled, around which computational grids using random triangulation are generated. The RKDG method, in its development stage, was constructed and studied for solving hyperbolic conservation equations numerically. It was later extended to multidimensional nonlinear systems of conservation laws. The algorithms are described, including the formulations and treatments to the numerical fluxes, degrees of freedom, boundary conditions, and other implementation issues. The computational solution amounts to a near-field solution in form of contour plot and one extending from the scatterer to a far-field boundary located a few wavelengths away. Near-field to far-field transformation utilizing the Green's function is performed to obtain the bistatic radar cross section information. Results are presented for scatterings from a series of two-dimensional objects, including circular and square cylinders, ogive and NACA airfoils. Also, scatterings from more complex geometries such as cylindrical and rectangular cavitations are simulated. Exact solutions for selected cases are compared to the computational results and demonstrate excellent accuracy and efficiency in the RKDG calculations. In the whole, its ease and flexibility to incorporate the characteristic-based schemes for the flux integrals between cell interfaces, and the compact formulation allowing direct application to the boundary elements without modification are some of the admired features of the DG method.

Variance of discharge estimates sampled using acoustic Doppler current profilers from moving boats

USGS Publications Warehouse

Garcia, Carlos M.; Tarrab, Leticia; Oberg, Kevin; Szupiany, Ricardo; Cantero, Mariano I.

2012-01-01

This paper presents a model for quantifying the random errors (i.e., variance) of acoustic Doppler current profiler (ADCP) discharge measurements from moving boats for different sampling times. The model focuses on the random processes in the sampled flow field and has been developed using statistical methods currently available for uncertainty analysis of velocity time series. Analysis of field data collected using ADCP from moving boats from three natural rivers of varying sizes and flow conditions shows that, even though the estimate of the integral time scale of the actual turbulent flow field is larger than the sampling interval, the integral time scale of the sampled flow field is on the order of the sampling interval. Thus, an equation for computing the variance error in discharge measurements associated with different sampling times, assuming uncorrelated flow fields is appropriate. The approach is used to help define optimal sampling strategies by choosing the exposure time required for ADCPs to accurately measure flow discharge.

Electron in higher-dimensional weakly charged rotating black hole spacetimes

NASA Astrophysics Data System (ADS)

Cariglia, Marco; Frolov, Valeri P.; Krtouš, Pavel; Kubizňák, David

2013-03-01

We demonstrate separability of the Dirac equation in weakly charged rotating black hole spacetimes in all dimensions. The electromagnetic field of the black hole is described by a test field approximation, with the vector potential proportional to the primary Killing vector field. It is shown that the demonstrated separability can be intrinsically characterized by the existence of a complete set of mutually commuting first-order symmetry operators generated from the principal Killing-Yano tensor. The presented results generalize the results on integrability of charged particle motion and separability of charged scalar field studied in V. P. Frolov and P. Krtous [Phys. Rev. D 83, 024016 (2011)].

Dynamics of a differential-difference integrable (2+1)-dimensional system.

PubMed

Yu, Guo-Fu; Xu, Zong-Wei

2015-06-01

A Kadomtsev-Petviashvili- (KP-) type equation appears in fluid mechanics, plasma physics, and gas dynamics. In this paper, we propose an integrable semidiscrete analog of a coupled (2+1)-dimensional system which is related to the KP equation and the Zakharov equation. N-soliton solutions of the discrete equation are presented. Some interesting examples of soliton resonance related to the two-soliton and three-soliton solutions are investigated. Numerical computations using the integrable semidiscrete equation are performed. It is shown that the integrable semidiscrete equation gives very accurate numerical results in the cases of one-soliton evolution and soliton interactions.

Topics in Bethe Ansatz

NASA Astrophysics Data System (ADS)

Wang, Chunguang

Integrable quantum spin chains have close connections to integrable quantum field. theories, modern condensed matter physics, string and Yang-Mills theories. Bethe. ansatz is one of the most important approaches for solving quantum integrable spin. chains. At the heart of the algebraic structure of integrable quantum spin chains is. the quantum Yang-Baxter equation and the boundary Yang-Baxter equation. This. thesis focuses on four topics in Bethe ansatz. The Bethe equations for the isotropic periodic spin-1/2 Heisenberg chain with N. sites have solutions containing ±i/2 that are singular: both the corresponding energy and the algebraic Bethe ansatz vector are divergent. Such solutions must be carefully regularized. We consider a regularization involving a parameter that can be. determined using a generalization of the Bethe equations. These generalized Bethe. equations provide a practical way of determining which singular solutions correspond. to eigenvectors of the model. The Bethe equations for the periodic XXX and XXZ spin chains admit singular. solutions, for which the corresponding eigenvalues and eigenvectors are ill-defined. We use a twist regularization to derive conditions for such singular solutions to bephysical, in which case they correspond to genuine eigenvalues and eigenvectors of. the Hamiltonian. We analyze the ground state of the open spin-1/2 isotropic quantum spin chain. with a non-diagonal boundary term using a recently proposed Bethe ansatz solution. As the coefficient of the non-diagonal boundary term tends to zero, the Bethe roots. split evenly into two sets: those that remain finite, and those that become infinite. We. argue that the former satisfy conventional Bethe equations, while the latter satisfy a. generalization of the Richardson-Gaudin equations. We derive an expression for the. leading correction to the boundary energy in terms of the boundary parameters. We argue that the Hamiltonians for A(2) 2n open quantum spin chains corresponding. to two choices of integrable boundary conditions have the symmetries Uq(Bn) and. Uq(Cn), respectively. The deformation of Cn is novel, with a nonstandard coproduct. We find a formula for the Dynkin labels of the Bethe states (which determine the degeneracies of the corresponding eigenvalues) in terms of the numbers of Bethe roots of. each type. With the help of this formula, we verify numerically (for a generic value of. the anisotropy parameter) that the degeneracies and multiplicities of the spectra implied by the quantum group symmetries are completely described by the Bethe ansatz.

A systematic study of finite BRST-BFV transformations in Sp(2)-extended generalized Hamiltonian formalism

NASA Astrophysics Data System (ADS)

Batalin, Igor A.; Lavrov, Peter M.; Tyutin, Igor V.

2014-09-01

We study systematically finite BRST-BFV transformations in Sp(2)-extended generalized Hamiltonian formalism. We present explicitly their Jacobians and the form of a solution to the compensation equation determining the functional field dependence of finite Fermionic parameters, necessary to generate arbitrary finite change of gauge-fixing functions in the path integral.

Particle paths and phase plane for time-dependent similarity solutions of the one-dimensional Vlasov-Maxwell equations

NASA Technical Reports Server (NTRS)

Roberts, Dana Aaron; Abraham-Shrauner, Barbara

1987-01-01

The phase trajectories of particles in a plasma described by the one-dimensional Vlasov-Maxwell equations are determined qualitatively, analyzing exact general similarity solutions for the cases of temporally damped and growing (sinusoidal or localized) electric fields. The results of numerical integration in both untransformed and Lie-group point-transformed coordinates are presented in extensive graphs and characterized in detail. The implications of the present analysis for the stability of BGK equilibria are explored, and the existence of nonlinear solutions arbitrarily close to and significantly different from the BGK solutions is demonstrated.

A Fourier collocation time domain method for numerically solving Maxwell's equations

NASA Technical Reports Server (NTRS)

Shebalin, John V.

1991-01-01

A new method for solving Maxwell's equations in the time domain for arbitrary values of permittivity, conductivity, and permeability is presented. Spatial derivatives are found by a Fourier transform method and time integration is performed using a second order, semi-implicit procedure. Electric and magnetic fields are collocated on the same grid points, rather than on interleaved points, as in the Finite Difference Time Domain (FDTD) method. Numerical results are presented for the propagation of a 2-D Transverse Electromagnetic (TEM) mode out of a parallel plate waveguide and into a dielectric and conducting medium.

Elementary functions in thermodynamic Bethe ansatz

NASA Astrophysics Data System (ADS)

Suzuki, J.

2015-05-01

Some years ago, Fendley found an explicit solution to the thermodynamic Bethe ansatz (TBA) equation for an N=2 supersymmetric theory in 2D with a specific F-term. Motivated by this, we seek explicit solutions for other super-potential cases utilizing the idea from the ODE/IM correspondence. We find that the TBA equations, corresponding to a wider class of super-potentials, admit solutions in terms of elementary functions such as modified Bessel functions and confluent hyper-geometric series. Based on talks given at ‘Infinite Analysis 2014’ (Tokyo, 2014) and at ‘Integrable lattice models and quantum field theories’ (Bad Honnef, 2014).

Stochastic layer scaling in the two-wire model for divertor tokamaks

NASA Astrophysics Data System (ADS)

Ali, Halima; Punjabi, Alkesh; Boozer, Allen

2009-06-01

The question of magnetic field structure in the vicinity of the separatrix in divertor tokamaks is studied. The authors have investigated this problem earlier in a series of papers, using various mathematical techniques. In the present paper, the two-wire model (TWM) [Reiman, A. 1996 Phys. Plasmas 3, 906] is considered. It is noted that, in the TWM, it is useful to consider an extra equation expressing magnetic flux conservation. This equation does not add any more information to the TWM, since the equation is derived from the TWM. This equation is useful for controlling the step size in the numerical integration of the TWM equations. The TWM with the extra equation is called the flux-preserving TWM. Nevertheless, the technique is apparently still plagued by numerical inaccuracies when the perturbation level is low, resulting in an incorrect scaling of the stochastic layer width. The stochastic broadening of the separatrix in the flux-preserving TWM is compared with that in the low mn (poloidal mode number m and toroidal mode number n) map (LMN) [Ali, H., Punjabi, A., Boozer, A. and Evans, T. 2004 Phys. Plasmas 11, 1908]. The flux-preserving TWM and LMN both give Boozer-Rechester 0.5 power scaling of the stochastic layer width with the amplitude of magnetic perturbation when the perturbation is sufficiently large [Boozer, A. and Rechester, A. 1978, Phys. Fluids 21, 682]. The flux-preserving TWM gives a larger stochastic layer width when the perturbation is low, while the LMN gives correct scaling in the low perturbation region. Area-preserving maps such as the LMN respect the Hamiltonian structure of field line trajectories, and have the added advantage of computational efficiency. Also, for a $1\\frac12$ degree of freedom Hamiltonian system such as field lines, maps do not give Arnold diffusion.

Two-dimensional integrating matrices on rectangular grids. [solving differential equations associated with rotating structures

NASA Technical Reports Server (NTRS)

Lakin, W. D.

1981-01-01

The use of integrating matrices in solving differential equations associated with rotating beam configurations is examined. In vibration problems, by expressing the equations of motion of the beam in matrix notation, utilizing the integrating matrix as an operator, and applying the boundary conditions, the spatial dependence is removed from the governing partial differential equations and the resulting ordinary differential equations can be cast into standard eigenvalue form. Integrating matrices are derived based on two dimensional rectangular grids with arbitrary grid spacings allowed in one direction. The derivation of higher dimensional integrating matrices is the initial step in the generalization of the integrating matrix methodology to vibration and stability problems involving plates and shells.

A far-field non-reflecting boundary condition for two-dimensional wake flows

NASA Technical Reports Server (NTRS)

Danowitz, Jeffrey S.; Abarbanel, Saul A.; Turkel, Eli

1995-01-01

Far-field boundary conditions for external flow problems have been developed based upon long-wave perturbations of linearized flow equations about a steady state far field solution. The boundary improves convergence to steady state in single-grid temporal integration schemes using both regular-time-stepping and local-time-stepping. The far-field boundary may be near the trailing edge of the body which significantly reduces the number of grid points, and therefore the computational time, in the numerical calculation. In addition the solution produced is smoother in the far-field than when using extrapolation conditions. The boundary condition maintains the convergence rate to steady state in schemes utilizing multigrid acceleration.

On geodynamo integrations conserving momentum flux

NASA Astrophysics Data System (ADS)

Wu, C.; Roberts, P. H.

2012-12-01

The equations governing the geodynamo are most often integrated by representing the magnetic field and fluid velocity by toroidal and poloidal scalars (for example, MAG code [1]). This procedure does not automatically conserve the momentum flux. The results can, particularly for flows with large shear, introduce significant errors, unless the viscosity is artificially increased. We describe a method that evades this difficulty, by solving the momentum equation directly while properly conserving momentum. It finds pressure by FFT and cyclic reduction, and integrates the governing equations on overlapping grids so avoiding the pole problem. The number of operations per time step is proportional to N3 where N is proportional to the number of grid points in each direction. This contrasts with the order N4 operations of standard spectral transform methods. The method is easily parallelized. It can also be easily adapted to schemes such as the Weighted Essentially Non-Oscillatory (WENO) method [2], a flux based procedure based on upwinding that is numerically stable even for zero explicit viscosity. The method has been successfully used to investigate the generation of magnetic fields by flows confined to spheroidal containers and driven by precessional and librational forcing [3, 4]. For spherical systems it satisfies dynamo benchmarks [5]. [1] MAG, http://www.geodynamics.org/cig/software/mag [2] Liu, XD, Osher, S and Chan, T, Weighted Essentially Nonoscillatory Schemes, J. Computational Physics, 115, 200-212, 1994. [3] Wu, CC and Roberts, PH, On a dynamo driven by topographic precession, Geophysical & Astrophysical Fluid Dynamics, 103, 467-501, (DOI: 10.1080/03091920903311788), 2009. [4] Wu, CC and Roberts, PH, On a dynamo driven topographically by longitudinal libration, Geophysical & Astrophysical Fluid Dynamics, DOI:10.1080/03091929.2012.682990, 2012. [5] Christensen, U, et al., A numerical dynamo benchmark, Phys. Earth Planet Int., 128, 25-34, 2001.

Gravitational radiation from compact binary systems: Gravitational waveforms and energy loss to second post-Newtonian order

NASA Astrophysics Data System (ADS)

Will, Clifford M.; Wiseman, Alan G.

1996-10-01

We derive the gravitational waveform and gravitational-wave energy flux generated by a binary star system of compact objects (neutron stars or black holes), accurate through second post-Newtonian order (O[(v/c)4]=O[(Gm/rc2)2]) beyond the lowest-order quadrupole approximation. We cast the Einstein equations into the form of a flat-spacetime wave equation together with a harmonic gauge condition, and solve it formally as a retarded integral over the past null cone of the chosen field point. The part of this integral that involves the matter sources and the near-zone gravitational field is evaluated in terms of multipole moments using standard techniques; the remainder of the retarded integral, extending over the radiation zone, is evaluated in a novel way. The result is a manifestly convergent and finite procedure for calculating gravitational radiation to arbitrary orders in a post-Newtonian expansion. Through second post-Newtonian order, the radiation is also shown to propagate toward the observer along true null rays of the asymptotically Schwarzschild spacetime, despite having been derived using flat-spacetime wave equations. The method cures defects that plagued previous ``brute-force'' slow-motion approaches to the generation of gravitational radiation, and yields results that agree perfectly with those recently obtained by a mixed post-Minkowskian post-Newtonian method. We display explicit formulas for the gravitational waveform and the energy flux for two-body systems, both in arbitrary orbits and in circular orbits. In an appendix, we extend the formalism to bodies with finite spatial extent, and derive the spin corrections to the waveform and energy loss.

Nonlinear Field Equations and Solitons as Particles

NASA Astrophysics Data System (ADS)

Maccari, Attilio

2006-05-01

Profound advances have recently interested nonlinear field theories and their exact or approximate solutions. We review the last results and point out some important unresolved questions. It is well known that quantum field theories are based upon Fourier series and the identification of plane waves with free particles. On the contrary, nonlinear field theories admit the existence of coherent solutions (dromions, solitons and so on). Moreover, one can construct lower dimensional chaotic patterns, periodic-chaotic patterns, chaotic soliton and dromion patterns. In a similar way, fractal dromion and lump patterns as well as stochastic fractal excitations can appear in the solution. We discuss in some detail a nonlinear Dirac field and a spontaneous symmetry breaking model that are reduced by means of the asymptotic perturbation method to a system of nonlinear evolution equations integrable via an appropriate change of variables. Their coherent, chaotic and fractal solutions are examined in some detail. Finally, we consider the possible identification of some types of coherent solutions with extended particles along the de Broglie-Bohm theory. However, the last findings suggest an inadequacy of the particle concept that appears only as a particular case of nonlinear field theories excitations.

Assessing potential scour using the South Carolina bridge-scour envelope curves

USGS Publications Warehouse

Benedict, Stephen T.; Feaster, Toby D.; Caldwell, Andral W.

2016-09-30

SummaryBridge-scour equations presented in the Federal Highway Administration Hydraulic Engineering Circular No. 18 reflect the current state-of-the practice for predicting scour at bridges. Although these laboratory-derived equations provide an important resource for assessing scour potential, there is a measure of uncertainty when applying these equations to field conditions. The uncertainty and limitations have been acknowledged by laboratory researchers and confirmed in field investigations.Because of the uncertainty associated with bridge-scour equations, HEC-18 recommends that engineers evaluate the computed scour depths obtained from the equations and modify the resulting data if they appear unreasonable. Perhaps the best way to evaluate the reasonableness of predicted scour is to compare it to field measurements of historic scour. Historic field data show scour depths resulting from high flows and provide a reference for evaluating predicted scour. It is rare, however, that such data are available at or near a site of interest, making the evaluation of predicted scour as compared to field data difficult if not impossible. Realizing the value of historic scour measurements, the U.S. Geological Survey (USGS), in cooperation with the South Carolina Department of Transportation (SCDOT), conducted a series of three field investigations to collect historic scour data with the goal of understanding regional trends of scour at riverine bridges in South Carolina.Historic scour measurements, including measurements of clear-water abutment, contraction, and pier scour, as well as live-bed contraction and pier scour, were made at more than 200 bridges. These field investigations provided valuable insights into regional scour trends and yielded regional bridge-scour envelope curves that can be used as supplementary tools for assessing all components of scour at riverine bridges in South Carolina.The application and limitations of these envelope curves were documented in four reports. Because each report addresses different components of bridge scour, it was recognized that there was a need to develop an integrated procedure for applying the envelope curves to help assess scour potential at riverine bridges in South Carolina. The result of that effort is detailed in Benedict and others (2016) and summarized in this fact sheet.

The space-time solution element method: A new numerical approach for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Scott, James R.; Chang, Sin-Chung

1995-01-01

This paper is one of a series of papers describing the development of a new numerical method for the Navier-Stokes equations. Unlike conventional numerical methods, the current method concentrates on the discrete simulation of both the integral and differential forms of the Navier-Stokes equations. Conservation of mass, momentum, and energy in space-time is explicitly provided for through a rigorous enforcement of both the integral and differential forms of the governing conservation laws. Using local polynomial expansions to represent the discrete primitive variables on each cell, fluxes at cell interfaces are evaluated and balanced using exact functional expressions. No interpolation or flux limiters are required. Because of the generality of the current method, it applies equally to the steady and unsteady Navier-Stokes equations. In this paper, we generalize and extend the authors' 2-D, steady state implicit scheme. A general closure methodology is presented so that all terms up through a given order in the local expansions may be retained. The scheme is also extended to nonorthogonal Cartesian grids. Numerous flow fields are computed and results are compared with known solutions. The high accuracy of the scheme is demonstrated through its ability to accurately resolve developing boundary layers on coarse grids. Finally, we discuss applications of the current method to the unsteady Navier-Stokes equations.

Accurate D-bar Reconstructions of Conductivity Images Based on a Method of Moment with Sinc Basis.

PubMed

Abbasi, Mahdi

2014-01-01

Planar D-bar integral equation is one of the inverse scattering solution methods for complex problems including inverse conductivity considered in applications such as Electrical impedance tomography (EIT). Recently two different methodologies are considered for the numerical solution of D-bar integrals equation, namely product integrals and multigrid. The first one involves high computational burden and the other one suffers from low convergence rate (CR). In this paper, a novel high speed moment method based using the sinc basis is introduced to solve the two-dimensional D-bar integral equation. In this method, all functions within D-bar integral equation are first expanded using the sinc basis functions. Then, the orthogonal properties of their products dissolve the integral operator of the D-bar equation and results a discrete convolution equation. That is, the new moment method leads to the equation solution without direct computation of the D-bar integral. The resulted discrete convolution equation maybe adapted to a suitable structure to be solved using fast Fourier transform. This allows us to reduce the order of computational complexity to as low as O (N (2)log N). Simulation results on solving D-bar equations arising in EIT problem show that the proposed method is accurate with an ultra-linear CR.

Geometry, Heat Equation and Path Integrals on the Poincaré Upper Half-Plane

NASA Astrophysics Data System (ADS)

Kubo, R.

1988-01-01

Geometry, heat equation and Feynman's path integrals are studied on the Poincaré upper half-plane. The fundamental solution to the heat equation partial f/partial t = Delta_{H} f is expressed in terms of a path integral defined on the upper half-plane. It is shown that Kac's statement that Feynman's path integral satisfies the Schrödinger equation is also valid for our case.

Effective long wavelength scalar dynamics in de Sitter

DOE Office of Scientific and Technical Information (OSTI.GOV)

Moss, Ian; Rigopoulos, Gerasimos, E-mail: ian.moss@newcastle.ac.uk, E-mail: gerasimos.rigopoulos@ncl.ac.uk

We discuss the effective infrared theory governing a light scalar's long wavelength dynamics in de Sitter spacetime. We show how the separation of scales around the physical curvature radius k / a ∼ H can be performed consistently with a window function and how short wavelengths can be integrated out in the Schwinger-Keldysh path integral formalism. At leading order, and for time scales Δ t >> H {sup −1}, this results in the well-known Starobinsky stochastic evolution. However, our approach allows for the computation of quantum UV corrections, generating an effective potential on which the stochastic dynamics takes place. Themore » long wavelength stochastic dynamical equations are now second order in time, incorporating temporal scales Δ t ∼ H {sup −1} and resulting in a Kramers equation for the probability distribution—more precisely the Wigner function—in contrast to the more usual Fokker-Planck equation. This feature allows us to non-perturbatively evaluate, within the stochastic formalism, not only expectation values of field correlators, but also the stress-energy tensor of φ.« less

Two-and-one-half-dimensional magnetohydrodynamic simulations of the plasma sheet in the presence of oxygen ions: The plasma sheet oscillation and compressional Pc 5 waves

NASA Astrophysics Data System (ADS)

Lu, Li; Liu, Zhen-Xing; Cao, Jin-Bin

2002-02-01

Two-and-one-half-dimensional magnetohydrodynamic simulations of the multicomponent plasma sheet with the velocity curl term in the magnetic equation are represented. The simulation results can be summarized as follows: (1) There is an oscillation of the plasma sheet with the period on the order of 400 s (Pc 5 range); (2) the magnetic equator is a node of the magnetic field disturbance; (3) the magnetic energy integral varies antiphase with the internal energy integral; (4) disturbed waves have a propagating speed on the order of 10 km/s earthward; (5) the abundance of oxygen ions influences amplitude, period, and dissipation of the plasma sheet oscillation. It is suggested that the compressional Pc 5 waves, which are observed in the plasma sheet close to the magnetic equator, may be caused by the plasma sheet oscillation, or may be generated from the resonance of the plasma sheet oscillation with some Pc 5 perturbation waves coming from the outer magnetosphere.

Rapid calculation of acoustic fields from arbitrary continuous-wave sources.

PubMed

Treeby, Bradley E; Budisky, Jakub; Wise, Elliott S; Jaros, Jiri; Cox, B T

2018-01-01

A Green's function solution is derived for calculating the acoustic field generated by phased array transducers of arbitrary shape when driven by a single frequency continuous wave excitation with spatially varying amplitude and phase. The solution is based on the Green's function for the homogeneous wave equation expressed in the spatial frequency domain or k-space. The temporal convolution integral is solved analytically, and the remaining integrals are expressed in the form of the spatial Fourier transform. This allows the acoustic pressure for all spatial positions to be calculated in a single step using two fast Fourier transforms. The model is demonstrated through several numerical examples, including single element rectangular and spherically focused bowl transducers, and multi-element linear and hemispherical arrays.

Modeling global vector fields of chaotic systems from noisy time series with the aid of structure-selection techniques.

PubMed

Xu, Daolin; Lu, Fangfang

2006-12-01

We address the problem of reconstructing a set of nonlinear differential equations from chaotic time series. A method that combines the implicit Adams integration and the structure-selection technique of an error reduction ratio is proposed for system identification and corresponding parameter estimation of the model. The structure-selection technique identifies the significant terms from a pool of candidates of functional basis and determines the optimal model through orthogonal characteristics on data. The technique with the Adams integration algorithm makes the reconstruction available to data sampled with large time intervals. Numerical experiment on Lorenz and Rossler systems shows that the proposed strategy is effective in global vector field reconstruction from noisy time series.

Non-autonomous multi-rogue waves for spin-1 coupled nonlinear Gross-Pitaevskii equation and management by external potentials.

PubMed

Li, Li; Yu, Fajun

2017-09-06

We investigate non-autonomous multi-rogue wave solutions in a three-component(spin-1) coupled nonlinear Gross-Pitaevskii(GP) equation with varying dispersions, higher nonlinearities, gain/loss and external potentials. The similarity transformation allows us to relate certain class of multi-rogue wave solutions of the spin-1 coupled nonlinear GP equation to the solutions of integrable coupled nonlinear Schrödinger(CNLS) equation. We study the effect of time-dependent quadratic potential on the profile and dynamic of non-autonomous rogue waves. With certain requirement on the backgrounds, some non-autonomous multi-rogue wave solutions exhibit the different shapes with two peaks and dip in bright-dark rogue waves. Then, the managements with external potential and dynamic behaviors of these solutions are investigated analytically. The results could be of interest in such diverse fields as Bose-Einstein condensates, nonlinear fibers and super-fluids.

Solution of the exact equations for three-dimensional atmospheric entry using directly matched asymptotic expansions

NASA Technical Reports Server (NTRS)

Busemann, A.; Vinh, N. X.; Culp, R. D.

1976-01-01

The problem of determining the trajectories, partially or wholly contained in the atmosphere of a spherical, nonrotating planet, is considered. The exact equations of motion for three-dimensional, aerodynamically affected flight are derived. Modified Chapman variables are introduced and the equations are transformed into a set suitable for analytic integration using asymptotic expansions. The trajectory is solved in two regions: the outer region, where the force may be considered a gravitational field with aerodynamic perturbations, and the inner region, where the force is predominantly aerodynamic, with gravity as a perturbation. The two solutions are matched directly. A composite solution, valid everywhere, is constructed by additive composition. This approach of directly matched asymptotic expansions applied to the exact equations of motion couched in terms of modified Chapman variables yields an analytical solution which should prove to be a powerful tool for aerodynamic orbit calculations.

Exact PDF equations and closure approximations for advective-reactive transport

DOE Office of Scientific and Technical Information (OSTI.GOV)

Venturi, D.; Tartakovsky, Daniel M.; Tartakovsky, Alexandre M.

2013-06-01

Mathematical models of advection–reaction phenomena rely on advective flow velocity and (bio) chemical reaction rates that are notoriously random. By using functional integral methods, we derive exact evolution equations for the probability density function (PDF) of the state variables of the advection–reaction system in the presence of random transport velocity and random reaction rates with rather arbitrary distributions. These PDF equations are solved analytically for transport with deterministic flow velocity and a linear reaction rate represented mathematically by a heterog eneous and strongly-correlated random field. Our analytical solution is then used to investigate the accuracy and robustness of the recentlymore » proposed large-eddy diffusivity (LED) closure approximation [1]. We find that the solution to the LED-based PDF equation, which is exact for uncorrelated reaction rates, is accurate even in the presence of strong correlations and it provides an upper bound of predictive uncertainty.« less

Modeling of thin-walled structures interacting with acoustic media as constrained two-dimensional continua

NASA Astrophysics Data System (ADS)

Rabinskiy, L. N.; Zhavoronok, S. I.

2018-04-01

The transient interaction of acoustic media and elastic shells is considered on the basis of the transition function approach. The three-dimensional hyperbolic initial boundary-value problem is reduced to a two-dimensional problem of shell theory with integral operators approximating the acoustic medium effect on the shell dynamics. The kernels of these integral operators are determined by the elementary solution of the problem of acoustic waves diffraction at a rigid obstacle with the same boundary shape as the wetted shell surface. The closed-form elementary solution for arbitrary convex obstacles can be obtained at the initial interaction stages on the background of the so-called “thin layer hypothesis”. Thus, the shell–wave interaction model defined by integro-differential dynamic equations with analytically determined kernels of integral operators becomes hence two-dimensional but nonlocal in time. On the other hand, the initial interaction stage results in localized dynamic loadings and consequently in complex strain and stress states that require higher-order shell theories. Here the modified theory of I.N.Vekua–A.A.Amosov-type is formulated in terms of analytical continuum dynamics. The shell model is constructed on a two-dimensional manifold within a set of field variables, Lagrangian density, and constraint equations following from the boundary conditions “shifted” from the shell faces to its base surface. Such an approach allows one to construct consistent low-order shell models within a unified formal hierarchy. The equations of the N th-order shell theory are singularly perturbed and contain second-order partial derivatives with respect to time and surface coordinates whereas the numerical integration of systems of first-order equations is more efficient. Such systems can be obtained as Hamilton–de Donder–Weyl-type equations for the Lagrangian dynamical system. The Hamiltonian formulation of the elementary N th-order shell theory is here briefly described.

Experimental and numerical modelling of surface water-groundwater flow and pollution interactions under tidal forcing

NASA Astrophysics Data System (ADS)

Spanoudaki, Katerina; Bockelmann-Evans, Bettina; Schaefer, Florian; Kampanis, Nikolaos; Nanou-Giannarou, Aikaterini; Stamou, Anastasios; Falconer, Roger

2015-04-01

Surface water and groundwater are integral components of the hydrologic continuum and the interaction between them affects both their quantity and quality. However, surface water and groundwater are often considered as two separate systems and are analysed independently. This separation is partly due to the different time scales, which apply in surface water and groundwater flows and partly due to the difficulties in measuring and modelling their interactions (Winter et al., 1998). Coastal areas in particular are a difficult hydrologic environment to represent with a mathematical model due to the large number of contributing hydrologic processes. Accurate prediction of interactions between coastal waters, groundwater and neighbouring wetlands, for example, requires the use of integrated surface water-groundwater models. In the past few decades a large number of mathematical models and field methods have been developed in order to quantify the interaction between groundwater and hydraulically connected surface water bodies. Field studies may provide the best data (Hughes, 1995) but are usually expensive and involve too many parameters. In addition, the interpretation of field measurements and linking with modelling tools often proves to be difficult. In contrast, experimental studies are less expensive and provide controlled data. However, experimental studies of surface water-groundwater interaction are less frequently encountered in the literature than filed studies (e.g. Ebrahimi et al., 2007; Kuan et al., 2012; Sparks et al., 2013). To this end, an experimental model has been constructed at the Hyder Hydraulics Laboratory at Cardiff University to enable measurements to be made of groundwater transport through a sand embankment between a tidal water body such as an estuary and a non-tidal water body such as a wetland. The transport behaviour of a conservative tracer was studied for a constant water level on the wetland side of the embankment, while running a continuous tide on the coastal side. The integrated surface water-groundwater numerical model IRENE (Spanoudaki et al., 2009, Spanoudaki, 2010) was also used in the study, with the numerical model predictions being compared with experimental results, which provide a valuable database for model calibration and validation. IRENE couples the 3D, non-steady state Navier-Stokes equations, after Reynolds averaging and with the assumption of hydrostatic pressure distribution, to the equations describing 3D saturated groundwater flow of constant density. The model uses the finite volume method with a cell-centered structured grid providing thus flexibility and accuracy in simulating irregular boundary geometries. A semi-implicit finite difference scheme is used to solve the surface water flow equations, while a fully implicit finite difference scheme is used for the groundwater equations. Pollution interactions are simulated by coupling the advection-diffusion equation describing the fate and transport of contaminants introduced in a 3D turbulent flow field to the partial differential equation describing the fate and transport of contaminants in 3D transient groundwater flow systems. References Ebrahimi, K., Falconer, R.A. and Lin B. (2007). Flow and solute fluxes in integrated wetland and coastal systems. Environmental Modelling and Software, 22 (9), 1337-1348. Hughes, S.A. (1995). Physical Modelling and Laboratory Techniques in Coastal Engineering. World Scientific Publishing Co. Pte. Ltd., Singapore. Kuan, W.K., Jin, G., Xin, P., Robinson, C. Gibbes, B. and Li. L. (2012). Tidal influence on seawater intrusion in unconfined coastal aquifers. Water Resources Research, 48 (2), doi:10.1029/2011WR010678. Spanoudaki, K., Stamou, A.I. and Nanou-Giannarou, A. (2009). Development and verification of a 3-D integrated surface water-groundwater model. Journal of Hydrology, 375 (3-4), 410-427. Spanoudaki, K. (2010). Integrated numerical modelling of surface water groundwater systems (in Greek). Ph.D. Thesis, National Technical University of Athens, Greece. Sparks, T. D., Bockelmann-Evans, B. N. and Falconer, R. A. (2013). Laboratory Validation of an Integrated Surface Water- Groundwater Model. Journal of Water Resource and Protection, 5, 377-394. Winter, T.C., Harvey, J.W., Franke, O.L. and Alley, W.M., 1998. Groundwater and surface water - A single resource. USGS, Circular 1139.

Building analytical three-field cosmological models

NASA Astrophysics Data System (ADS)

Santos, J. R. L.; Moraes, P. H. R. S.; Ferreira, D. A.; Neta, D. C. Vilar

2018-02-01

A difficult task to deal with is the analytical treatment of models composed of three real scalar fields, as their equations of motion are in general coupled and hard to integrate. In order to overcome this problem we introduce a methodology to construct three-field models based on the so-called "extension method". The fundamental idea of the procedure is to combine three one-field systems in a non-trivial way, to construct an effective three scalar field model. An interesting scenario where the method can be implemented is with inflationary models, where the Einstein-Hilbert Lagrangian is coupled with the scalar field Lagrangian. We exemplify how a new model constructed from our method can lead to non-trivial behaviors for cosmological parameters.

Two-soliton interaction as an elementary act of soliton turbulence in integrable systems

NASA Astrophysics Data System (ADS)

Pelinovsky, E. N.; Shurgalina, E. G.; Sergeeva, A. V.; Talipova, T. G.; El, G. A.; Grimshaw, R. H. J.

2013-01-01

Two-soliton interactions play a definitive role in the formation of the structure of soliton turbulence in integrable systems. To quantify the contribution of these interactions to the dynamical and statistical characteristics of the nonlinear wave field of soliton turbulence we study properties of the spatial moments of the two-soliton solution of the Korteweg-de Vries (KdV) equation. While the first two moments are integrals of the KdV evolution, the 3rd and 4th moments undergo significant variations in the dominant interaction region, which could have strong effect on the values of the skewness and kurtosis in soliton turbulence.

Field induced transient current in one-dimensional nanostructure

NASA Astrophysics Data System (ADS)

Sako, Tokuei; Ishida, Hiroshi

2018-07-01

Field-induced transient current in one-dimensional nanostructures has been studied by a model of an electron confined in a 1D attractive Gaussian potential subjected both to electrodes at the terminals and to an ultrashort pulsed oscillatory electric field with the central frequency ω and the FWHM pulse width Γ. The time-propagation of the electron wave packet has been simulated by integrating the time-dependent Schrödinger equation directly relying on the second-order symplectic integrator method. The transient current has been calculated as the flux of the probability density of the escaping wave packet emitted from the downstream side of the confining potential. When a static bias-field E0 is suddenly applied, the resultant transient current shows an oscillatory decay behavior with time followed by a minimum structure before converging to a nearly constant value. The ω-dependence of the integrated transient current induced by the pulsed electric field has shown an asymmetric resonance line-shape for large Γ while it shows a fringe pattern on the spectral line profile for small Γ. These observations have been rationalized on the basis of the energy-level structure and lifetime of the quasibound states in the bias-field modified confining potential obtained by the complex-scaling Fourier grid Hamiltonian method.

Squared eigenfunctions for the Sasa-Satsuma equation

NASA Astrophysics Data System (ADS)

Yang, Jianke; Kaup, D. J.

2009-02-01

Squared eigenfunctions are quadratic combinations of Jost functions and adjoint Jost functions which satisfy the linearized equation of an integrable equation. They are needed for various studies related to integrable equations, such as the development of its soliton perturbation theory. In this article, squared eigenfunctions are derived for the Sasa-Satsuma equation whose spectral operator is a 3×3 system, while its linearized operator is a 2×2 system. It is shown that these squared eigenfunctions are sums of two terms, where each term is a product of a Jost function and an adjoint Jost function. The procedure of this derivation consists of two steps: First is to calculate the variations of the potentials via variations of the scattering data by the Riemann-Hilbert method. The second one is to calculate the variations of the scattering data via the variations of the potentials through elementary calculations. While this procedure has been used before on other integrable equations, it is shown here, for the first time, that for a general integrable equation, the functions appearing in these variation relations are precisely the squared eigenfunctions and adjoint squared eigenfunctions satisfying, respectively, the linearized equation and the adjoint linearized equation of the integrable system. This proof clarifies this procedure and provides a unified explanation for previous results of squared eigenfunctions on individual integrable equations. This procedure uses primarily the spectral operator of the Lax pair. Thus two equations in the same integrable hierarchy will share the same squared eigenfunctions (except for a time-dependent factor). In the Appendix, the squared eigenfunctions are presented for the Manakov equations whose spectral operator is closely related to that of the Sasa-Satsuma equation.

A Unified Treatment of the Acoustic and Elastic Scattered Waves from Fluid-Elastic Media

NASA Astrophysics Data System (ADS)

Denis, Max Fernand

In this thesis, contributions are made to the numerical modeling of the scattering fields from fluid-filled poroelastic materials. Of particular interest are highly porous materials that demonstrate strong contrast to the saturating fluid. A Biot's analysis of porous medium serves as the starting point of the elastic-solid and pore-fluid governing equations of motion. The longitudinal scattering waves of the elastic-solid mode and the pore-fluid mode are modeled by the Kirchhoff-Helmholtz integral equation. The integral equation is evaluated using a series approximation, describing the successive perturbation of the material contrasts. To extended the series' validity into larger domains, rational fraction extrapolation methods are employed. The local Pade□ approximant procedure is a technique that allows one to extrapolate from a scattered field of small contrast into larger values, using Pade□ approximants. To ensure the accuracy of the numerical model, comparisons are made with the exact solution of scattering from a fluid sphere. Mean absolute error analyses, yield convergent and accurate results. In addition, the numerical model correctly predicts the Bragg peaks for a periodic lattice of fluid spheres. In the case of trabecular bones, the far-field scattering pressure attenuation is a superposition of the elastic-solid mode and the pore-fluid mode generated waves from the surrounding fluid and poroelastic boundaries. The attenuation is linearly dependent with frequency between 0.2 and 0.6MHz. The slope of the attenuation is nonlinear with porosity, and does not reflect the mechanical properties of the trabecular bone. The attenuation shows the anisotropic effects of the trabeculae structure. Thus, ultrasound can possibly be employed to non-invasively predict the principal structural orientation of trabecular bones.

Regularized quasinormal modes for plasmonic resonators and open cavities

NASA Astrophysics Data System (ADS)

Kamandar Dezfouli, Mohsen; Hughes, Stephen

2018-03-01

Optical mode theory and analysis of open cavities and plasmonic particles is an essential component of optical resonator physics, offering considerable insight and efficiency for connecting to classical and quantum optical properties such as the Purcell effect. However, obtaining the dissipative modes in normalized form for arbitrarily shaped open-cavity systems is notoriously difficult, often involving complex spatial integrations, even after performing the necessary full space solutions to Maxwell's equations. The formal solutions are termed quasinormal modes, which are known to diverge in space, and additional techniques are frequently required to obtain more accurate field representations in the far field. In this work, we introduce a finite-difference time-domain technique that can be used to obtain normalized quasinormal modes using a simple dipole-excitation source, and an inverse Green function technique, in real frequency space, without having to perform any spatial integrations. Moreover, we show how these modes are naturally regularized to ensure the correct field decay behavior in the far field, and thus can be used at any position within and outside the resonator. We term these modes "regularized quasinormal modes" and show the reliability and generality of the theory by studying the generalized Purcell factor of dipole emitters near metallic nanoresonators, hybrid devices with metal nanoparticles coupled to dielectric waveguides, as well as coupled cavity-waveguides in photonic crystals slabs. We also directly compare our results with full-dipole simulations of Maxwell's equations without any approximations, and show excellent agreement.

Mathematical Methods for Physics and Engineering Third Edition Paperback Set

NASA Astrophysics Data System (ADS)

Riley, Ken F.; Hobson, Mike P.; Bence, Stephen J.

2006-06-01

Prefaces; 1. Preliminary algebra; 2. Preliminary calculus; 3. Complex numbers and hyperbolic functions; 4. Series and limits; 5. Partial differentiation; 6. Multiple integrals; 7. Vector algebra; 8. Matrices and vector spaces; 9. Normal modes; 10. Vector calculus; 11. Line, surface and volume integrals; 12. Fourier series; 13. Integral transforms; 14. First-order ordinary differential equations; 15. Higher-order ordinary differential equations; 16. Series solutions of ordinary differential equations; 17. Eigenfunction methods for differential equations; 18. Special functions; 19. Quantum operators; 20. Partial differential equations: general and particular; 21. Partial differential equations: separation of variables; 22. Calculus of variations; 23. Integral equations; 24. Complex variables; 25. Application of complex variables; 26. Tensors; 27. Numerical methods; 28. Group theory; 29. Representation theory; 30. Probability; 31. Statistics; Index.

Theory and observation of electromagnetic ion cyclotron triggered emissions in the magnetosphere

NASA Astrophysics Data System (ADS)

Omura, Yoshiharu; Pickett, Jolene; Grison, Benjamin; Santolik, Ondrej; Dandouras, Iannis; Engebretson, Mark; Décréau, Pierrette M. E.; Masson, Arnaud

2010-07-01

We develop a nonlinear wave growth theory of electromagnetic ion cyclotron (EMIC) triggered emissions observed in the inner magnetosphere. We first derive the basic wave equations from Maxwell's equations and the momentum equations for the electrons and ions. We then obtain equations that describe the nonlinear dynamics of resonant protons interacting with an EMIC wave. The frequency sweep rate of the wave plays an important role in forming the resonant current that controls the wave growth. Assuming an optimum condition for the maximum growth rate as an absolute instability at the magnetic equator and a self-sustaining growth condition for the wave propagating from the magnetic equator, we obtain a set of ordinary differential equations that describe the nonlinear evolution of a rising tone emission generated at the magnetic equator. Using the physical parameters inferred from the wave, particle, and magnetic field data measured by the Cluster spacecraft, we determine the dispersion relation for the EMIC waves. Integrating the differential equations numerically, we obtain a solution for the time variation of the amplitude and frequency of a rising tone emission at the equator. Assuming saturation of the wave amplitude, as is found in the observations, we find good agreement between the numerical solutions and the wave spectrum of the EMIC triggered emissions.

Exact Mass-Coupling Relation for the Homogeneous Sine-Gordon Model.

PubMed

Bajnok, Zoltán; Balog, János; Ito, Katsushi; Satoh, Yuji; Tóth, Gábor Zsolt

2016-05-06

We derive the exact mass-coupling relation of the simplest multiscale quantum integrable model, i.e., the homogeneous sine-Gordon model with two mass scales. The relation is obtained by comparing the perturbed conformal field theory description of the model valid at short distances to the large distance bootstrap description based on the model's integrability. In particular, we find a differential equation for the relation by constructing conserved tensor currents, which satisfy a generalization of the Θ sum rule Ward identity. The mass-coupling relation is written in terms of hypergeometric functions.

A Maxwell-Schrödinger solver for quantum optical few-level systems

NASA Astrophysics Data System (ADS)

Fleischhaker, Robert; Evers, Jörg

2011-03-01

The msprop program presented in this work is capable of solving the Maxwell-Schrödinger equations for one or several laser fields propagating through a medium of quantum optical few-level systems in one spatial dimension and in time. In particular, it allows to numerically treat systems in which a laser field interacts with the medium with both its electric and magnetic component at the same time. The internal dynamics of the few-level system is modeled by a quantum optical master equation which includes coherent processes due to optical transitions driven by the laser fields as well as incoherent processes due to decay and dephasing. The propagation dynamics of the laser fields is treated in slowly varying envelope approximation resulting in a first order wave equation for each laser field envelope function. The program employs an Adams predictor formula second order in time to integrate the quantum optical master equation and a Lax-Wendroff scheme second order in space and time to evolve the wave equations for the fields. The source function in the Lax-Wendroff scheme is specifically adapted to allow taking into account the simultaneous coupling of a laser field to the polarization and the magnetization of the medium. To reduce execution time, a customized data structure is implemented and explained. In three examples the features of the program are demonstrated and the treatment of a system with a phase-dependent cross coupling of the electric and magnetic field component of a laser field is shown. Program summaryProgram title: msprop Catalogue identifier: AEHR_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHR_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 507 625 No. of bytes in distributed program, including test data, etc.: 10 698 552 Distribution format: tar.gz Programming language: C (C99 standard), Mathematica, bash script, gnuplot script Computer: Tested on x86 architecture Operating system: Unix/Linux environment RAM: Less than 30 MB Classification: 2.5 External routines: Standard C math library, accompanying bash script uses gnuplot, bc (basic calculator), and convert (ImageMagick) Nature of problem: We consider a system of quantum optical few-level atoms exposed to several near-resonant continuous-wave or pulsed laser fields. The complexity of the problem arises from the combination of the coherent and incoherent time evolution of the atoms and its dependence on the spatially varying fields. In systems with a coupling to the electric and magnetic field component the simultaneous treatment of both field components poses an additional challenge. Studying the system dynamics requires solving the quantum optical master equation coupled to the wave equations governing the spatio-temporal dynamics of the fields [1,2]. Solution method: We numerically integrate the equations of motion using a second order Adams predictor method for the time evolution of the atomic density matrix and a second order Lax-Wendroff scheme for iterating the fields in space [3]. For the Lax-Wendroff scheme, the source function is adapted such that a simultaneous coupling to the polarization and the magnetization of the medium can be taken into account. Restrictions: The evolution of the fields is treated in slowly varying envelope approximation [2] such that variations of the fields in space and time must be on a scale larger than the wavelength and the optical cycle. Propagation is restricted to the forward direction and to one dimension. Concerning the description of the atomic system, only a finite number of basis states can be treated and the laser-driven transitions have to be near-resonant such that the rotating-wave approximation can be applied [2]. Unusual features: The program allows the dipole interaction of both the electric and the magnetic component of a laser field to be taken into account at the same time. Thus, a system with a phase-dependent cross coupling of electric and magnetic field component can be treated (see Section 4.2 and [4]). Concerning the implementation of the data structure, it has been optimized for faster memory access. Compared to using standard memory allocation methods, shorter run times are achieved (see Section 3.2). Additional comments: Three examples are given. They each include a readme file, a Mathematica notebook to generate the C-code form of the quantum optical master equation, a parameter file, a bash script which runs the program and converts the numerical data into a movie, two gnuplot scripts, and all files that are produced by running the bash script. Running time: For the first two examples the running time is less than a minute, the third example takes about 12 minutes. On a Pentium 4 (3 GHz) system, a rough estimate can be made with a value of 1 second per million grid points and per field variable.

Dynamics of Vortex and Magnetic Lines in Ideal Hydrodynamics and MHD

NASA Astrophysics Data System (ADS)

Kuznetsov, E. A.; Ruban, V. P.

Vortex line and magnetic line representations are introduced for description of flows in ideal hydrodynamics and MHD, respectively. For incompressible fluids it is shown that the equations of motion for vorticity φ and magnetic field with the help of this transformation follow from the variational principle. By means of this representation it is possible to integrate the system of hydrodynamic type with the Hamiltonian H=|φ|dr. It is also demonstrated that these representations allow to remove from the noncanonical Poisson brackets, defined on the space of divergence-free vector fields, degeneracy connected with the vorticity frozenness for the Euler equation and with magnetic field frozenness for ideal MHD. For MHD a new Weber type transformation is found. It is shown how this transformation can be obtained from the two-fluid model when electrons and ions can be considered as two independent fluids. The Weber type transformation for ideal MHD gives the whole Lagrangian vector invariant. When this invariant is absent this transformation coincides with the Clebsch representation analog introduced in [1].

Application of closed-form solutions to a mesh point field in silicon solar cells

NASA Technical Reports Server (NTRS)

Lamorte, M. F.

1985-01-01

A computer simulation method is discussed that provides for equivalent simulation accuracy, but that exhibits significantly lower CPU running time per bias point compared to other techniques. This new method is applied to a mesh point field as is customary in numerical integration (NI) techniques. The assumption of a linear approximation for the dependent variable, which is typically used in the finite difference and finite element NI methods, is not required. Instead, the set of device transport equations is applied to, and the closed-form solutions obtained for, each mesh point. The mesh point field is generated so that the coefficients in the set of transport equations exhibit small changes between adjacent mesh points. Application of this method to high-efficiency silicon solar cells is described; and the method by which Auger recombination, ambipolar considerations, built-in and induced electric fields, bandgap narrowing, carrier confinement, and carrier diffusivities are treated. Bandgap narrowing has been investigated using Fermi-Dirac statistics, and these results show that bandgap narrowing is more pronounced and that it is temperature-dependent in contrast to the results based on Boltzmann statistics.

Hybrid reconstruction of field-reversed configurations

NASA Astrophysics Data System (ADS)

Steinhauer, Loren; TAE Team

2016-10-01

Field-reversed configurations (FRC) are poorly represented by fluid-based models and require instead an ion-distribution function. Two such populations are needed since ``core'' ions are roughly restricted to the region inside the separatrix, whereas ``periphery'' ions can escape along open field lines. The Vlasov equation governs the distribution, the general solution to which is an arbitrary function of the constants of motion (Hamiltonian, canonical angular momentum). Only a small subset of such distributions are realistic in view of collisions, which smooth the distribution, and instabilities, which reorganize the field structure. Collisions and end loss are included if the distribution is a solution to the Fokker-Planck (FP) equation. Vlasov and FP solutions are nearly identical in weakly-collisional plasmas. Numerical construction of such equilibria requires solving both Ampere's law for the magnetic flux variable and the ponderous task of a full velocity-space integration at each point. The latter can be done analytically by expressing the distribution as the superposition of simple basis elements. This procedure allows rapid reconstruction of evolving equilibria based on limited diagnostic observables in FRC experiments.

Coprimeness-preserving non-integrable extension to the two-dimensional discrete Toda lattice equation

NASA Astrophysics Data System (ADS)

Kamiya, Ryo; Kanki, Masataka; Mase, Takafumi; Tokihiro, Tetsuji

2017-01-01

We introduce a so-called coprimeness-preserving non-integrable extension to the two-dimensional Toda lattice equation. We believe that this equation is the first example of such discrete equations defined over a three-dimensional lattice. We prove that all the iterates of the equation are irreducible Laurent polynomials of the initial data and that every pair of two iterates is co-prime, which indicate confined singularities of the equation. By reducing the equation to two- or one-dimensional lattices, we obtain coprimeness-preserving non-integrable extensions to the one-dimensional Toda lattice equation and the Somos-4 recurrence.

An Equation-Free Reduced-Order Modeling Approach to Tropical Pacific Simulation

NASA Astrophysics Data System (ADS)

Wang, Ruiwen; Zhu, Jiang; Luo, Zhendong; Navon, I. M.

2009-03-01

The “equation-free” (EF) method is often used in complex, multi-scale problems. In such cases it is necessary to know the closed form of the required evolution equations about oscopic variables within some applied fields. Conceptually such equations exist, however, they are not available in closed form. The EF method can bypass this difficulty. This method can obtain oscopic information by implementing models at a microscopic level. Given an initial oscopic variable, through lifting we can obtain the associated microscopic variable, which may be evolved using Direct Numerical Simulations (DNS) and by restriction, we can obtain the necessary oscopic information and the projective integration to obtain the desired quantities. In this paper we apply the EF POD-assisted method to the reduced modeling of a large-scale upper ocean circulation in the tropical Pacific domain. The computation cost is reduced dramatically. Compared with the POD method, the method provided more accurate results and it did not require the availability of any explicit equations or the right-hand side (RHS) of the evolution equation.

Group invariant solutions of the Ernst equation of general relativity theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pryse, P.V.

The local symmetry group of the Ernst Equation for stationary, axisymmetric, vacuum space-time manifolds is computed by application of the method of Olver. Several implicit solutions of the equation are found by use of this group. Each of these solutions is given in terms of a function defined as a solution of an ordinary differential equation. One of these equations is integrated by quadratures by use of its own local symmetry group, the result being three explicit solutions of the Ernst Equation. For one of these solutions the metric of the space-time manifold is constructed and studied. The solutions hasmore » a ring curvature singularity and it is asymptotically flat in the sense that the curvature invariants approach zero at spatial infinity. The timelike and null geodesics on the symmetry axis and in the plane of the ring singularity are described. The test particles following these geodesics are seen to be repelled by the ring, which suggests the interpretation of this solution as representing the exterior gravitational field of a rotating ring of matter with negative gravitational mass.« less

Scattering from a cylindrical reflector: modified theory of physical optics solution.

PubMed

Yalçin, Ugur

2007-02-01

The problem of scattering from a perfectly conducting cylindrical reflector is examined with the method of the modified theory of physical optics. In this technique the physical optics currents are modified by using a variable unit vector on the scatterer's surface. These current components are obtained for the reflector, which is fed by an offset electric line source. The scattering integral is expressed by using these currents and evaluated asymptotically with the stationary phase method. The results are compared numerically by using physical optics theory, geometrical optics diffraction theory, and the exact solution of the Helmholtz equation. It is found that the modified theory of physical optics scattering field equations agrees with the geometrical optics diffraction theory and the exact solution of the Helmholtz equation.

Eulerian Simulation of Acoustic Waves Over Long Range in Realistic Environments

NASA Astrophysics Data System (ADS)

Chitta, Subhashini; Steinhoff, John

2015-11-01

In this paper, we describe a new method for computation of long-range acoustics. The approach is a hybrid of near and far-field methods, and is unique in its Eulerian treatment of the far-field propagation. The near-field generated by any existing method to project an acoustic solution onto a spherical surface that surrounds a source. The acoustic field on this source surface is then extended to an arbitrarily large distance in an inhomogeneous far-field. This would normally require an Eulerian solution of the wave equation. However, conventional Eulerian methods have prohibitive grid requirements. This problem is overcome by using a new method, ``Wave Confinement'' (WC) that propagates wave-identifying phase fronts as nonlinear solitary waves that live on grid indefinitely. This involves modification of wave equation by the addition of a nonlinear term without changing the basic conservation properties of the equation. These solitary waves can then be used to ``carry'' the essential integrals of the acoustic wave. For example, arrival time, centroid position and other properties that are invariant as the wave passes a grid point. Because of this property the grid can be made as coarse as necessary, consistent with overall accuracy to resolve atmospheric/ground variations. This work is being funded by the U.S. Army under a Small Business Innovation Research (SBIR) program (contract number: # W911W6-12-C-0036). The authors would like to thank Dr. Frank Caradonna and Dr. Ben W. Sim for this support.

Auxiliary field loop expansion of the effective action for a class of stochastic partial differential equations

NASA Astrophysics Data System (ADS)

Cooper, Fred; Dawson, John F.

2016-02-01

We present an alternative to the perturbative (in coupling constant) diagrammatic approach for studying stochastic dynamics of a class of reaction diffusion systems. Our approach is based on an auxiliary field loop expansion for the path integral representation for the generating functional of the noise induced correlation functions of the fields describing these systems. The systems we consider include Langevin systems describable by the set of self interacting classical fields ϕi(x , t) in the presence of external noise ηi(x , t) , namely (∂t - ν∇2) ϕ - F [ ϕ ] = η, as well as chemical reaction annihilation processes obtained by applying the many-body approach of Doi-Peliti to the Master Equation formulation of these problems. We consider two different effective actions, one based on the Onsager-Machlup (OM) approach, and the other due to Janssen-deGenneris based on the Martin-Siggia-Rose (MSR) response function approach. For the simple models we consider, we determine an analytic expression for the Energy landscape (effective potential) in both formalisms and show how to obtain the more physical effective potential of the Onsager-Machlup approach from the MSR effective potential in leading order in the auxiliary field loop expansion. For the KPZ equation we find that our approximation, which is non-perturbative and obeys broken symmetry Ward identities, does not lead to the appearance of a fluctuation induced symmetry breakdown. This contradicts the results of earlier studies.

Geometric foundations of the theory of feedback equivalence

NASA Technical Reports Server (NTRS)

Hermann, R.

1987-01-01

A description of feedback control is presented within the context of differential equations, differential geometry, and Lie theory. Work related to the integration of differential geometry with the control techniques of feedback linearization is summarized. Particular attention is given to the application of the theory of vector field systems. Feedback invariants for control systems in state space form are also addressed.

Analytic study of a rolling sphere on a rough surface

NASA Astrophysics Data System (ADS)

Florea, Olivia A.; Rosca, Ileana C.

2016-11-01

In this paper it is realized an analytic study of the rolling's sphere on a rough horizontal plane under the action of its own gravity. The necessities of integration of the system of dynamical equations of motion lead us to find a reference system where the motion equations should be transformed into simpler expressions and which, in the presence of some significant hypothesis to permit the application of some original methods of analytical integration. In technical applications, the bodies may have a free rolling motion or a motion constrained by geometrical relations in assemblies of parts and machine parts. This study involves a lot of investigations in the field of tribology and of applied dynamics accompanied by experiments. Multiple recordings of several trajectories of the sphere, as well as their treatment of images, also followed by statistical processing experimental data allowed highlighting a very good agreement between the theoretical findings and experimental results.

Momentum conserving defects in affine Toda field theories

NASA Astrophysics Data System (ADS)

Bristow, Rebecca; Bowcock, Peter

2017-05-01

Type II integrable defects with more than one degree of freedom at the defect are investigated. A condition on the form of the Lagrangian for such defects is found which ensures the existence of a conserved momentum in the presence of the defect. In addition it is shown that for any Lagrangian satisfying this condition, the defect equations of motion, when taken to hold everywhere, can be extended to give a Bäcklund transformation between the bulk theories on either side of the defect. This strongly suggests that such systems are integrable. Momentum conserving defects and Bäcklund transformations for affine Toda field theories based on the A n , B n , C n and D n series of Lie algebras are found. The defect associated with the D 4 affine Toda field theory is examined in more detail. In particular classical time delays for solitons passing through the defect are calculated.

A hybrid framework of first principles molecular orbital calculations and a three-dimensional integral equation theory for molecular liquids: Multi-center molecular Ornstein-Zernike self-consistent field approach

NASA Astrophysics Data System (ADS)

Kido, Kentaro; Kasahara, Kento; Yokogawa, Daisuke; Sato, Hirofumi

2015-07-01

In this study, we reported the development of a new quantum mechanics/molecular mechanics (QM/MM)-type framework to describe chemical processes in solution by combining standard molecular-orbital calculations with a three-dimensional formalism of integral equation theory for molecular liquids (multi-center molecular Ornstein-Zernike (MC-MOZ) method). The theoretical procedure is very similar to the 3D-reference interaction site model self-consistent field (RISM-SCF) approach. Since the MC-MOZ method is highly parallelized for computation, the present approach has the potential to be one of the most efficient procedures to treat chemical processes in solution. Benchmark tests to check the validity of this approach were performed for two solute (solute water and formaldehyde) systems and a simple SN2 reaction (Cl- + CH3Cl → ClCH3 + Cl-) in aqueous solution. The results for solute molecular properties and solvation structures obtained by the present approach were in reasonable agreement with those obtained by other hybrid frameworks and experiments. In particular, the results of the proposed approach are in excellent agreements with those of 3D-RISM-SCF.

A hybrid framework of first principles molecular orbital calculations and a three-dimensional integral equation theory for molecular liquids: multi-center molecular Ornstein-Zernike self-consistent field approach.

PubMed

Kido, Kentaro; Kasahara, Kento; Yokogawa, Daisuke; Sato, Hirofumi

2015-07-07

In this study, we reported the development of a new quantum mechanics/molecular mechanics (QM/MM)-type framework to describe chemical processes in solution by combining standard molecular-orbital calculations with a three-dimensional formalism of integral equation theory for molecular liquids (multi-center molecular Ornstein-Zernike (MC-MOZ) method). The theoretical procedure is very similar to the 3D-reference interaction site model self-consistent field (RISM-SCF) approach. Since the MC-MOZ method is highly parallelized for computation, the present approach has the potential to be one of the most efficient procedures to treat chemical processes in solution. Benchmark tests to check the validity of this approach were performed for two solute (solute water and formaldehyde) systems and a simple SN2 reaction (Cl(-) + CH3Cl → ClCH3 + Cl(-)) in aqueous solution. The results for solute molecular properties and solvation structures obtained by the present approach were in reasonable agreement with those obtained by other hybrid frameworks and experiments. In particular, the results of the proposed approach are in excellent agreements with those of 3D-RISM-SCF.

Numerical and experimental investigation on static electric charge model at stable cone-jet region

NASA Astrophysics Data System (ADS)

Hashemi, Ali Reza; Pishevar, Ahmad Reza; Valipouri, Afsaneh; Pǎrǎu, Emilian I.

2018-03-01

In a typical electro-spinning process, the steady stretching process of the jet beyond the Taylor cone has a significant effect on the dimensions of resulting nanofibers. Also, it sets up the conditions for the onset of the bending instability. The focus of this work is the modeling and simulation of the initial stable jet phase seen during the electro-spinning process. The perturbation method was applied to solve hydrodynamic equations, and the electrostatic equation was solved by a boundary integral method. These equations were coupled with the stress boundary conditions derived appropriate at the fluid-fluid interface. Perturbation equations were discretized by the second-order finite difference method, and the Newton method was implemented to solve the discretized nonlinear system. Also, the boundary element method was utilized to solve the electrostatic equation. In the theoretical study, the fluid is described as a leaky dielectric with charges only on the jet surface in dielectric air. In this study, electric charges were modeled as static. Comparison of numerical and experimental results shows that at low flow rates and high electric field, good agreement was achieved because of the superior importance of the charge transport by conduction rather than convection and charge concentration. In addition, the effect of unevenness of the electric field around the nozzle tip was experimentally studied through plate-plate geometry as well as point-plate geometry.

Fredholm-Volterra Integral Equation with a Generalized Singular Kernel and its Numerical Solutions

NASA Astrophysics Data System (ADS)

El-Kalla, I. L.; Al-Bugami, A. M.

2010-11-01

In this paper, the existence and uniqueness of solution of the Fredholm-Volterra integral equation (F-VIE), with a generalized singular kernel, are discussed and proved in the spaceL2(Ω)×C(0,T). The Fredholm integral term (FIT) is considered in position while the Volterra integral term (VIT) is considered in time. Using a numerical technique we have a system of Fredholm integral equations (SFIEs). This system of integral equations can be reduced to a linear algebraic system (LAS) of equations by using two different methods. These methods are: Toeplitz matrix method and Product Nyström method. A numerical examples are considered when the generalized kernel takes the following forms: Carleman function, logarithmic form, Cauchy kernel, and Hilbert kernel.

A principled dimension-reduction method for the population density approach to modeling networks of neurons with synaptic dynamics.

PubMed

Ly, Cheng

2013-10-01

The population density approach to neural network modeling has been utilized in a variety of contexts. The idea is to group many similar noisy neurons into populations and track the probability density function for each population that encompasses the proportion of neurons with a particular state rather than simulating individual neurons (i.e., Monte Carlo). It is commonly used for both analytic insight and as a time-saving computational tool. The main shortcoming of this method is that when realistic attributes are incorporated in the underlying neuron model, the dimension of the probability density function increases, leading to intractable equations or, at best, computationally intensive simulations. Thus, developing principled dimension-reduction methods is essential for the robustness of these powerful methods. As a more pragmatic tool, it would be of great value for the larger theoretical neuroscience community. For exposition of this method, we consider a single uncoupled population of leaky integrate-and-fire neurons receiving external excitatory synaptic input only. We present a dimension-reduction method that reduces a two-dimensional partial differential-integral equation to a computationally efficient one-dimensional system and gives qualitatively accurate results in both the steady-state and nonequilibrium regimes. The method, termed modified mean-field method, is based entirely on the governing equations and not on any auxiliary variables or parameters, and it does not require fine-tuning. The principles of the modified mean-field method have potential applicability to more realistic (i.e., higher-dimensional) neural networks.

Diffusive processes in a stochastic magnetic field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, H.; Vlad, M.; Vanden Eijnden, E.

1995-05-01

The statistical representation of a fluctuating (stochastic) magnetic field configuration is studied in detail. The Eulerian correlation functions of the magnetic field are determined, taking into account all geometrical constraints: these objects form a nondiagonal matrix. The Lagrangian correlations, within the reasonable Corrsin approximation, are reduced to a single scalar function, determined by an integral equation. The mean square perpendicular deviation of a geometrical point moving along a perturbed field line is determined by a nonlinear second-order differential equation. The separation of neighboring field lines in a stochastic magnetic field is studied. We find exponentiation lengths of both signs describing,more » in particular, a decay (on the average) of any initial anisotropy. The vanishing sum of these exponentiation lengths ensures the existence of an invariant which was overlooked in previous works. Next, the separation of a particle`s trajectory from the magnetic field line to which it was initially attached is studied by a similar method. Here too an initial phase of exponential separation appears. Assuming the existence of a final diffusive phase, anomalous diffusion coefficients are found for both weakly and strongly collisional limits. The latter is identical to the well known Rechester-Rosenbluth coefficient, which is obtained here by a more quantitative (though not entirely deductive) treatment than in earlier works.« less

Student Solution Manual for Mathematical Methods for Physics and Engineering Third Edition

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2006-03-01

Preface; 1. Preliminary algebra; 2. Preliminary calculus; 3. Complex numbers and hyperbolic functions; 4. Series and limits; 5. Partial differentiation; 6. Multiple integrals; 7. Vector algebra; 8. Matrices and vector spaces; 9. Normal modes; 10. Vector calculus; 11. Line, surface and volume integrals; 12. Fourier series; 13. Integral transforms; 14. First-order ordinary differential equations; 15. Higher-order ordinary differential equations; 16. Series solutions of ordinary differential equations; 17. Eigenfunction methods for differential equations; 18. Special functions; 19. Quantum operators; 20. Partial differential equations: general and particular; 21. Partial differential equations: separation of variables; 22. Calculus of variations; 23. Integral equations; 24. Complex variables; 25. Application of complex variables; 26. Tensors; 27. Numerical methods; 28. Group theory; 29. Representation theory; 30. Probability; 31. Statistics.

Full Wave Parallel Code for Modeling RF Fields in Hot Plasmas

NASA Astrophysics Data System (ADS)

Spencer, Joseph; Svidzinski, Vladimir; Evstatiev, Evstati; Galkin, Sergei; Kim, Jin-Soo

2015-11-01

FAR-TECH, Inc. is developing a suite of full wave RF codes in hot plasmas. It is based on a formulation in configuration space with grid adaptation capability. The conductivity kernel (which includes a nonlocal dielectric response) is calculated by integrating the linearized Vlasov equation along unperturbed test particle orbits. For Tokamak applications a 2-D version of the code is being developed. Progress of this work will be reported. This suite of codes has the following advantages over existing spectral codes: 1) It utilizes the localized nature of plasma dielectric response to the RF field and calculates this response numerically without approximations. 2) It uses an adaptive grid to better resolve resonances in plasma and antenna structures. 3) It uses an efficient sparse matrix solver to solve the formulated linear equations. The linear wave equation is formulated using two approaches: for cold plasmas the local cold plasma dielectric tensor is used (resolving resonances by particle collisions), while for hot plasmas the conductivity kernel is calculated. Work is supported by the U.S. DOE SBIR program.

Two-dimensional fast marching for geometrical optics.

PubMed

Capozzoli, Amedeo; Curcio, Claudio; Liseno, Angelo; Savarese, Salvatore

2014-11-03

We develop an approach for the fast and accurate determination of geometrical optics solutions to Maxwell's equations in inhomogeneous 2D media and for TM polarized electric fields. The eikonal equation is solved by the fast marching method. Particular attention is paid to consistently discretizing the scatterers' boundaries and matching the discretization to that of the computational domain. The ray tracing is performed, in a direct and inverse way, by using a technique introduced in computer graphics for the fast and accurate generation of textured images from vector fields. The transport equation is solved by resorting only to its integral form, the transport of polarization being trivial for the considered geometry and polarization. Numerical results for the plane wave scattering of two perfectly conducting circular cylinders and for a Luneburg lens prove the accuracy of the algorithm. In particular, it is shown how the approach is capable of properly accounting for the multiple scattering occurring between the two metallic cylinders and how inverse ray tracing should be preferred to direct ray tracing in the case of the Luneburg lens.

A new solution procedure for a nonlinear infinite beam equation of motion

NASA Astrophysics Data System (ADS)

Jang, T. S.

2016-10-01

Our goal of this paper is of a purely theoretical question, however which would be fundamental in computational partial differential equations: Can a linear solution-structure for the equation of motion for an infinite nonlinear beam be directly manipulated for constructing its nonlinear solution? Here, the equation of motion is modeled as mathematically a fourth-order nonlinear partial differential equation. To answer the question, a pseudo-parameter is firstly introduced to modify the equation of motion. And then, an integral formalism for the modified equation is found here, being taken as a linear solution-structure. It enables us to formulate a nonlinear integral equation of second kind, equivalent to the original equation of motion. The fixed point approach, applied to the integral equation, results in proposing a new iterative solution procedure for constructing the nonlinear solution of the original beam equation of motion, which consists luckily of just the simple regular numerical integration for its iterative process; i.e., it appears to be fairly simple as well as straightforward to apply. A mathematical analysis is carried out on both natures of convergence and uniqueness of the iterative procedure by proving a contractive character of a nonlinear operator. It follows conclusively,therefore, that it would be one of the useful nonlinear strategies for integrating the equation of motion for a nonlinear infinite beam, whereby the preceding question may be answered. In addition, it may be worth noticing that the pseudo-parameter introduced here has double roles; firstly, it connects the original beam equation of motion with the integral equation, second, it is related with the convergence of the iterative method proposed here.

Algebraic integrability: a survey.

PubMed

Vanhaecke, Pol

2008-03-28

We give a concise introduction to the notion of algebraic integrability. Our exposition is based on examples and phenomena, rather than on detailed proofs of abstract theorems. We mainly focus on algebraic integrability in the sense of Adler-van Moerbeke, where the fibres of the momentum map are affine parts of Abelian varieties; as it turns out, most examples from classical mechanics are of this form. Two criteria are given for such systems (Kowalevski-Painlevé and Lyapunov) and each is illustrated in one example. We show in the case of a relatively simple example how one proves algebraic integrability, starting from the differential equations for the integrable vector field. For Hamiltonian systems that are algebraically integrable in the generalized sense, two examples are given, which illustrate the non-compact analogues of Abelian varieties which typically appear in such systems.

A compressible Navier-Stokes solver with two-equation and Reynolds stress turbulence closure models

NASA Technical Reports Server (NTRS)

Morrison, Joseph H.

1992-01-01

This report outlines the development of a general purpose aerodynamic solver for compressible turbulent flows. Turbulent closure is achieved using either two equation or Reynolds stress transportation equations. The applicable equation set consists of Favre-averaged conservation equations for the mass, momentum and total energy, and transport equations for the turbulent stresses and turbulent dissipation rate. In order to develop a scheme with good shock capturing capabilities, good accuracy and general geometric capabilities, a multi-block cell centered finite volume approach is used. Viscous fluxes are discretized using a finite volume representation of a central difference operator and the source terms are treated as an integral over the control volume. The methodology is validated by testing the algorithm on both two and three dimensional flows. Both the two equation and Reynolds stress models are used on a two dimensional 10 degree compression ramp at Mach 3, and the two equation model is used on the three dimensional flow over a cone at angle of attack at Mach 3.5. With the development of this algorithm, it is now possible to compute complex, compressible high speed flow fields using both two equation and Reynolds stress turbulent closure models, with the capability of eventually evaluating their predictive performance.

A regularization method for extrapolation of solar potential magnetic fields

NASA Technical Reports Server (NTRS)

Gary, G. A.; Musielak, Z. E.

1992-01-01

The mathematical basis of a Tikhonov regularization method for extrapolating the chromospheric-coronal magnetic field using photospheric vector magnetograms is discussed. The basic techniques show that the Cauchy initial value problem can be formulated for potential magnetic fields. The potential field analysis considers a set of linear, elliptic partial differential equations. It is found that, by introducing an appropriate smoothing of the initial data of the Cauchy potential problem, an approximate Fourier integral solution is found, and an upper bound to the error in the solution is derived. This specific regularization technique, which is a function of magnetograph measurement sensitivities, provides a method to extrapolate the potential magnetic field above an active region into the chromosphere and low corona.

On flow of electrically conducting fluids over a flat plate in the presence of a transverse magnetic field

NASA Technical Reports Server (NTRS)

Rossow, Vernon J

1958-01-01

The use of a magnetic field to control the motion of electrically conducting fluids is studied. The incompressible boundary-layer solutions are found for flow over a flat plate when the magnetic field is fixed relative to the plate or to the fluid. The equations are integrated numerically for the effect of the transverse magnetic field on the velocity and temperature profiles, and hence, the skin friction and rate of heat transfer. It is concluded that the skin friction and the heat-transfer rate are reduced when the transverse magnetic field is fixed relative to the plate and increased when fixed relative to the fluid. The total drag is increased in all of the areas.

Algorithms for the computation of solutions of the Ornstein-Zernike equation.

PubMed

Peplow, A T; Beardmore, R E; Bresme, F

2006-10-01

We introduce a robust and efficient methodology to solve the Ornstein-Zernike integral equation using the pseudoarc length (PAL) continuation method that reformulates the integral equation in an equivalent but nonstandard form. This enables the computation of solutions in regions where the compressibility experiences large changes or where the existence of multiple solutions and so-called branch points prevents Newton's method from converging. We illustrate the use of the algorithm with a difficult problem that arises in the numerical solution of integral equations, namely the evaluation of the so-called no-solution line of the Ornstein-Zernike hypernetted chain (HNC) integral equation for the Lennard-Jones potential. We are able to use the PAL algorithm to solve the integral equation along this line and to connect physical and nonphysical solution branches (both isotherms and isochores) where appropriate. We also show that PAL continuation can compute solutions within the no-solution region that cannot be computed when Newton and Picard methods are applied directly to the integral equation. While many solutions that we find are new, some correspond to states with negative compressibility and consequently are not physical.

Integral equations in the study of polar and ionic interaction site fluids

PubMed Central

Howard, Jesse J.

2011-01-01

In this review article we consider some of the current integral equation approaches and application to model polar liquid mixtures. We consider the use of multidimensional integral equations and in particular progress on the theory and applications of three dimensional integral equations. The IEs we consider may be derived from equilibrium statistical mechanical expressions incorporating a classical Hamiltonian description of the system. We give example including salt solutions, inhomogeneous solutions and systems including proteins and nucleic acids. PMID:22383857

Oort's cloud evolution under the influence of the galactic field.

NASA Astrophysics Data System (ADS)

Kiryushenkova, N. V.; Chepurova, V. M.; Shershkina, S. L.

By numerical integration (Everhart's method) of the differential equations of cometary movement in Oort's cloud an attempt was made to observe how the galactic gravitational field changes the orbital elements of these comets during three solar revolutions in the Galaxy. It is shown that the cometary orbits are more elongated, even the initially circular orbits become strongly elliptical, in the outer layers of Oort's cloud it is possible for comets to turn into hyperbolic orbits and to leave the solar system. The boundaries of the solar system have been precised.

Refinement Of Hexahedral Cells In Euler Flow Computations

NASA Technical Reports Server (NTRS)

Melton, John E.; Cappuccio, Gelsomina; Thomas, Scott D.

1996-01-01

Topologically Independent Grid, Euler Refinement (TIGER) computer program solves Euler equations of three-dimensional, unsteady flow of inviscid, compressible fluid by numerical integration on unstructured hexahedral coordinate grid refined where necessary to resolve shocks and other details. Hexahedral cells subdivided, each into eight smaller cells, as needed to refine computational grid in regions of high flow gradients. Grid Interactive Refinement and Flow-Field Examination (GIRAFFE) computer program written in conjunction with TIGER program to display computed flow-field data and to assist researcher in verifying specified boundary conditions and refining grid.

A statistical formulation of one-dimensional electron fluid turbulence

NASA Technical Reports Server (NTRS)

Fyfe, D.; Montgomery, D.

1977-01-01

A one-dimensional electron fluid model is investigated using the mathematical methods of modern fluid turbulence theory. Non-dissipative equilibrium canonical distributions are determined in a phase space whose co-ordinates are the real and imaginary parts of the Fourier coefficients for the field variables. Spectral densities are calculated, yielding a wavenumber electric field energy spectrum proportional to k to the negative second power for large wavenumbers. The equations of motion are numerically integrated and the resulting spectra are found to compare well with the theoretical predictions.

Thermodynamic aspect in using modified Boltzmann model as an acoustic probe for URu2Si2

NASA Astrophysics Data System (ADS)

Kwang-Hua, Chu Rainer

2018-05-01

The approximate system of equations describing ultrasonic attenuation propagating in many electrons of the heavy-fermion materials URu2Si2 under high magnetic fields were firstly derived and then calculated based on the modified Boltzmann model considering the microscopic contributions due to electronic fluids. A system of nonlinear partial differential coupled with integral equations were linearized firstly and approximately solved considering the perturbed thermodynamic equilibrium states. Our numerical data were compared with previous measurements using non-dimensional or normalized physical values. The rather good fit of our numerical calculations with experimental measurements confirms our present approach.

Nonparaxial Dark-Hollow Gaussian Beams

NASA Astrophysics Data System (ADS)

Gao, Zeng-Hui; Lü, Bai-Da

2006-01-01

The concept of nonparaxial dark-hollow Gaussian beams (DHGBs) is introduced. By using the Rayleigh-Sommerfeld diffraction integral, the analytical propagation equation of DHGBs in free space is derived. The on-axis intensity, far-field equation and, in particular, paraxial expressions are given and treated as special cases of our result. It is shown that the parameter f = 1/kw0 with k being the wave number and w0 being the waist width determines the nonparaxiality of DHGBs. However, the parameter range, within which the paraxial approach is valid, depends on the propagation distance. The beam order affects the beam profile and position of maximum on-axis intensity.

A simple test for spacetime symmetry

NASA Astrophysics Data System (ADS)

Houri, Tsuyoshi; Yasui, Yukinori

2015-03-01

This paper presents a simple method for investigating spacetime symmetry for a given metric. The method makes use of the curvature conditions that are obtained from the Killing equations. We use the solutions of the curvature conditions to compute an upper bound on the number of Killing vector fields, as well as Killing-Yano (KY) tensors and closed conformal KY tensors. We also use them in the integration of the Killing equations. By means of the method, we thoroughly investigate KY symmetry of type D vacuum solutions such as the Kerr metric in four dimensions. The method is also applied to a large variety of physical metrics in four and five dimensions.

Stress intensity factors of composite orthotropic plates containing periodic buffer strips

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1978-01-01

The fracture problem of laminated plates which consist of bonded orthotropic layers is studied. The fields equations for an elastic orthotropic body are transformed to give the displacement and stress expressions for each layer or strip. The unknown functions in these expressions are found by satisfying the remaining boundary and continuity conditions. A system of singular integral equations is obtained from the mixed boundary conditions. The singular behavior around the crack tip and at the bimaterial interface is studied. The stress intensity factors are computed for various material combinations and various crack geometries. The results are discussed and are compared with those for isotropic materials.

Posterior quantum dynamics for a continuous diffusion observation of a coherent channel

NASA Astrophysics Data System (ADS)

Dąbrowska, Anita; Staszewski, Przemysław

2012-11-01

We present the Belavkin filtering equation for the intense balanced heterodyne detection in a unitary model of an indirect observation. The measuring apparatus modelled by a Bose field is initially prepared in a coherent state and the observed process is a diffusion one. We prove that this filtering equation is relaxing: any initial square-integrable function tends asymptotically to a coherent state with an amplitude depending on the coupling constant and the initial state of the apparatus. The time-development of a squeezed coherent state is studied and compared with the previous results obtained for the measuring apparatus prepared initially in the vacuum state.

Finite elements: Theory and application

NASA Technical Reports Server (NTRS)

Dwoyer, D. L. (Editor); Hussaini, M. Y. (Editor); Voigt, R. G. (Editor)

1988-01-01

Recent advances in FEM techniques and applications are discussed in reviews and reports presented at the ICASE/LaRC workshop held in Hampton, VA in July 1986. Topics addressed include FEM approaches for partial differential equations, mixed FEMs, singular FEMs, FEMs for hyperbolic systems, iterative methods for elliptic finite-element equations on general meshes, mathematical aspects of FEMS for incompressible viscous flows, and gradient weighted moving finite elements in two dimensions. Consideration is given to adaptive flux-corrected FEM transport techniques for CFD, mixed and singular finite elements and the field BEM, p and h-p versions of the FEM, transient analysis methods in computational dynamics, and FEMs for integrated flow/thermal/structural analysis.

A nonperturbative light-front coupled-cluster method

NASA Astrophysics Data System (ADS)

Hiller, J. R.

2012-10-01

The nonperturbative Hamiltonian eigenvalue problem for bound states of a quantum field theory is formulated in terms of Dirac's light-front coordinates and then approximated by the exponential-operator technique of the many-body coupled-cluster method. This approximation eliminates any need for the usual approximation of Fock-space truncation. Instead, the exponentiated operator is truncated, and the terms retained are determined by a set of nonlinear integral equations. These equations are solved simultaneously with an effective eigenvalue problem in the valence sector, where the number of constituents is small. Matrix elements can be calculated, with extensions of techniques from standard coupled-cluster theory, to obtain form factors and other observables.

A spectral boundary integral equation method for the 2-D Helmholtz equation

NASA Technical Reports Server (NTRS)

Hu, Fang Q.

1994-01-01

In this paper, we present a new numerical formulation of solving the boundary integral equations reformulated from the Helmholtz equation. The boundaries of the problems are assumed to be smooth closed contours. The solution on the boundary is treated as a periodic function, which is in turn approximated by a truncated Fourier series. A Fourier collocation method is followed in which the boundary integral equation is transformed into a system of algebraic equations. It is shown that in order to achieve spectral accuracy for the numerical formulation, the nonsmoothness of the integral kernels, associated with the Helmholtz equation, must be carefully removed. The emphasis of the paper is on investigating the essential elements of removing the nonsmoothness of the integral kernels in the spectral implementation. The present method is robust for a general boundary contour. Aspects of efficient implementation of the method using FFT are also discussed. A numerical example of wave scattering is given in which the exponential accuracy of the present numerical method is demonstrated.

Scattering models for some vegetation samples

NASA Technical Reports Server (NTRS)

Karam, M. A.; Fung, A. K.; Antar, Y. M. M.

1987-01-01

The Helmholtz integral equation is presently derived for a scatterer of arbitrary shape, and reduced in order to obtain the far zone-scattered field in terms of the field within the scatterer. Attention is given to the effect of different approaches to field estimation within the scatterer on the backscattering cross section, as illustrated numerically by the cases of a circular disk, a needle, and a finite-length cylinder. A comparison is made of the results obtained by modeling a leaf by means of a circular disk within the Shifrin approximation, and a tree branch by means of a finite-length cylinder, with measurements from a single leaf and a single branch.

Emergent spin electromagnetism induced by magnetization textures in the presence of spin-orbit interaction (invited)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tatara, Gen, E-mail: gen.tatara@riken.jp; Nakabayashi, Noriyuki; Graduate School of Science and Engineering, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397 Japan

2014-05-07

Emergent electromagnetic field which couples to electron's spin in ferromagnetic metals is theoretically studied. Rashba spin-orbit interaction induces spin electromagnetic field which is in the linear order in gradient of magnetization texture. The Rashba-induced effective electric and magnetic fields satisfy in the absence of spin relaxation the Maxwell's equations as in the charge-based electromagnetism. When spin relaxation is taken into account besides spin dynamics, a monopole current emerges generating spin motive force via the Faraday's induction law. The monopole is expected to play an important role in spin-charge conversion and in the integration of spintronics into electronics.

The application of the least squares finite element method to Abel's integral equation. [with application to glow discharge problem

NASA Technical Reports Server (NTRS)

Balasubramanian, R.; Norrie, D. H.; De Vries, G.

1979-01-01

Abel's integral equation is the governing equation for certain problems in physics and engineering, such as radiation from distributed sources. The finite element method for the solution of this non-linear equation is presented for problems with cylindrical symmetry and the extension to more general integral equations is indicated. The technique was applied to an axisymmetric glow discharge problem and the results show excellent agreement with previously obtained solutions

On one solution of Volterra integral equations of second kind

NASA Astrophysics Data System (ADS)

Myrhorod, V.; Hvozdeva, I.

2016-10-01

A solution of Volterra integral equations of the second kind with separable and difference kernels based on solutions of corresponding equations linking the kernel and resolvent is suggested. On the basis of a discrete functions class, the equations linking the kernel and resolvent are obtained and the methods of their analytical solutions are proposed. A mathematical model of the gas-turbine engine state modification processes in the form of Volterra integral equation of the second kind with separable kernel is offered.

A parameter study of the two-fluid solar wind

NASA Technical Reports Server (NTRS)

Sandbaek, Ornulf; Leer, Egil; Holzer, Thomas E.

1992-01-01

A two-fluid model of the solar wind was introduced by Sturrock and Hartle (1966) and Hartle and Sturrock (1968). In these studies the proton energy equation was integrated neglecting the heat conductive term. Later several authors solved the equations for the two-fluid solar wind model keeping the proton heat conductive term. Methods where the equations are integrated simultaneously outward and inward from the critical point were used. The equations were also integrated inward from a large heliocentric distance. These methods have been applied to cases with low coronal base electron densities and high base temperatures. In this paper we present a method of integrating the two-fluid solar wind equations using an iteration procedure where the equations are integrated separately and the proton flux is kept constant during the integrations. The technique is applicable for a wide range of coronal base densities and temperatures. The method is used to carry out a parameter study of the two-fluid solar wind.

Mean-field models for heterogeneous networks of two-dimensional integrate and fire neurons.

PubMed

Nicola, Wilten; Campbell, Sue Ann

2013-01-01

We analytically derive mean-field models for all-to-all coupled networks of heterogeneous, adapting, two-dimensional integrate and fire neurons. The class of models we consider includes the Izhikevich, adaptive exponential and quartic integrate and fire models. The heterogeneity in the parameters leads to different moment closure assumptions that can be made in the derivation of the mean-field model from the population density equation for the large network. Three different moment closure assumptions lead to three different mean-field systems. These systems can be used for distinct purposes such as bifurcation analysis of the large networks, prediction of steady state firing rate distributions, parameter estimation for actual neurons and faster exploration of the parameter space. We use the mean-field systems to analyze adaptation induced bursting under realistic sources of heterogeneity in multiple parameters. Our analysis demonstrates that the presence of heterogeneity causes the Hopf bifurcation associated with the emergence of bursting to change from sub-critical to super-critical. This is confirmed with numerical simulations of the full network for biologically reasonable parameter values. This change decreases the plausibility of adaptation being the cause of bursting in hippocampal area CA3, an area with a sizable population of heavily coupled, strongly adapting neurons.

Mean-field models for heterogeneous networks of two-dimensional integrate and fire neurons

PubMed Central

Nicola, Wilten; Campbell, Sue Ann

2013-01-01

We analytically derive mean-field models for all-to-all coupled networks of heterogeneous, adapting, two-dimensional integrate and fire neurons. The class of models we consider includes the Izhikevich, adaptive exponential and quartic integrate and fire models. The heterogeneity in the parameters leads to different moment closure assumptions that can be made in the derivation of the mean-field model from the population density equation for the large network. Three different moment closure assumptions lead to three different mean-field systems. These systems can be used for distinct purposes such as bifurcation analysis of the large networks, prediction of steady state firing rate distributions, parameter estimation for actual neurons and faster exploration of the parameter space. We use the mean-field systems to analyze adaptation induced bursting under realistic sources of heterogeneity in multiple parameters. Our analysis demonstrates that the presence of heterogeneity causes the Hopf bifurcation associated with the emergence of bursting to change from sub-critical to super-critical. This is confirmed with numerical simulations of the full network for biologically reasonable parameter values. This change decreases the plausibility of adaptation being the cause of bursting in hippocampal area CA3, an area with a sizable population of heavily coupled, strongly adapting neurons. PMID:24416013

Motion in a central field in the presence of a constant perturbing acceleration in a co-moving coordinate system

NASA Astrophysics Data System (ADS)

Sannikova, T. N.; Kholshevnikov, K. V.

2015-08-01

The motion of a point mass under the action of a gravitational force toward a central body and a perturbing acceleration P is considered. The magnitude of P is taken to be small compared to the main gravitational acceleration due to the central body, and the direction of P to be constant in a standard astronomical coordinate system with its origin at the central body and axes directed along the radius vector, the transversal, and the binormal. Consideration of a constant vector perturbing acceleration simplifies averaging of the Euler equations for the motion in osculating elements, making it straightforward to obtain evolutionary differential equations of motion in the mean elements, as was done earlier in a first small-parameter approximation. This paper is devoted to integration of the mean equations. The system is integratable by quadratures if at least one component of the perturbing acceleration is zero, and also if the orbit is initially circular. Moreover, all the quadratures can be expressed in terms of elementary functions and elliptical integrals of the first kind in Jacobi form. If all three components of P are non-zero, this problem reduces to a system of two first-order differential equations, which are apparently not integrable. Possible applications include the motion of natural and artificial satellites taking into account light pressure, the motion of a spacecraft with low thrust, and the motion of an asteroid subject to a thrust from an engine mounted on it or to a gravitational tractor designed, for example, to avoid a collision with Earth.

A curvature-corrected Kirchhoff formulation for radar sea-return from the near vertical

NASA Technical Reports Server (NTRS)

Jackson, F. C.

1974-01-01

A new theoretical treatment of the problem of electromagnetic wave scattering from a randomly rough surface is given. A high frequency correction to the Kirchhoff approximation is derived from a field integral equation for a perfectly conducting surface. The correction, which accounts for the effect of local surface curvature, is seen to be identical with an asymptotic form found by Fock (1945) for diffraction by a paraboloid. The corrected boundary values are substituted into the far field Stratton-Chu integral, and average backscattered powers are computed assuming the scattering surface is a homogeneous Gaussian process. Preliminary calculations for K(-4) ocean wave spectrum indicate a resonable modelling of polarization effects near the vertical, theta 45 deg. Correspondence with the results of small perturbation theory is shown.

Theoretical investigations of plasma processes in the ion bombardment thruster

NASA Technical Reports Server (NTRS)

Wilhelm, H. E.

1975-01-01

A physical model for a thruster discharge was developed, consisting of a spatially diverging plasma sustained electrically between a small ring cathode and a larger ring anode in a cylindrical chamber with an axial magnetic field. The associated boundary-value problem for the coupled partial differential equations with mixed boundary conditions, which describe the electric potential and the plasma velocity fields, was solved in closed form. By means of quantum-mechanical perturbation theory, a formula for the number S(E) of atoms sputtered on the average by an ion of energy E was derived from first principles. The boundary-value problem describing the diffusion of the sputtered atoms through the surrounding rarefied electron-ion plasma to the system surfaces of ion propulsion systems was formulated and treated analytically. It is shown that outer boundary-value problems of this type lead to a complex integral equation, which requires numerical resolution.

Adiabatic particle motion in a nearly drift-free magnetic field: Application to the geomagnetic tail

NASA Technical Reports Server (NTRS)

Stern, D. P.

1977-01-01

The guiding center motion of particles in a nearly drift free magnetic field is analyzed in order to investigate the dependence of mean drift velocity on equatorial pitch angle, the variation of local drift velocity along the trajectory, and other properties. The mean drift for adiabatic particles is expressed by means of elliptic integrals. Approximations to the twice-averaged Hamiltonian W near z = O are derived, permitting simple representation of drift paths if an electric potential also exists. In addition, the use of W or of expressions for the longitudinal invariant allows the derivation of the twice averaged Liouville equation and of the corresponding Vlasov equation. Bounce times are calculated (using the drift-free approximation), as are instantaneous guiding center drift velocities, which are then used to provide a numerical check on the formulas for the mean drift.

A multi-dimensional nonlinearly implicit, electromagnetic Vlasov-Darwin particle-in-cell (PIC) algorithm

NASA Astrophysics Data System (ADS)

Chen, Guangye; Chacón, Luis; CoCoMans Team

2014-10-01

For decades, the Vlasov-Darwin model has been recognized to be attractive for PIC simulations (to avoid radiative noise issues) in non-radiative electromagnetic regimes. However, the Darwin model results in elliptic field equations that renders explicit time integration unconditionally unstable. Improving on linearly implicit schemes, fully implicit PIC algorithms for both electrostatic and electromagnetic regimes, with exact discrete energy and charge conservation properties, have been recently developed in 1D. This study builds on these recent algorithms to develop an implicit, orbit-averaged, time-space-centered finite difference scheme for the particle-field equations in multiple dimensions. The algorithm conserves energy, charge, and canonical-momentum exactly, even with grid packing. A simple fluid preconditioner allows efficient use of large timesteps, O (√{mi/me}c/veT) larger than the explicit CFL. We demonstrate the accuracy and efficiency properties of the of the algorithm with various numerical experiments in 2D3V.

A Rate-Theory-Phase-Field Model of Irradiation-Induced Recrystallization in UMo Nuclear Fuels

NASA Astrophysics Data System (ADS)

Hu, Shenyang; Joshi, Vineet; Lavender, Curt A.

2017-12-01

In this work, we developed a recrystallization model to study the effect of microstructures and radiation conditions on recrystallization kinetics in UMo fuels. The model integrates the rate theory of intragranular gas bubble and interstitial loop evolutions and a phase-field model of recrystallization zone evolution. A first passage method is employed to describe one-dimensional diffusion of interstitials with a diffusivity value several orders of magnitude larger than that of fission gas xenons. With the model, the effect of grain sizes on recrystallization kinetics is simulated. The results show that (1) recrystallization in large grains starts earlier than that in small grains, (2) the recrystallization kinetics (recrystallization volume fraction) decrease as the grain size increases, (3) the predicted recrystallization kinetics are consistent with the experimental results, and (4) the recrystallization kinetics can be described by the modified Avrami equation, but the parameters of the Avrami equation strongly depend on the grain size.

The staircase method: integrals for periodic reductions of integrable lattice equations

NASA Astrophysics Data System (ADS)

van der Kamp, Peter H.; Quispel, G. R. W.

2010-11-01

We show, in full generality, that the staircase method (Papageorgiou et al 1990 Phys. Lett. A 147 106-14, Quispel et al 1991 Physica A 173 243-66) provides integrals for mappings, and correspondences, obtained as traveling wave reductions of (systems of) integrable partial difference equations. We apply the staircase method to a variety of equations, including the Korteweg-De Vries equation, the five-point Bruschi-Calogero-Droghei equation, the quotient-difference (QD)-algorithm and the Boussinesq system. We show that, in all these cases, if the staircase method provides r integrals for an n-dimensional mapping, with 2r, then one can introduce q <= 2r variables, which reduce the dimension of the mapping from n to q. These dimension-reducing variables are obtained as joint invariants of k-symmetries of the mappings. Our results support the idea that often the staircase method provides sufficiently many integrals for the periodic reductions of integrable lattice equations to be completely integrable. We also study reductions on other quad-graphs than the regular {\\ Z}^2 lattice, and we prove linear growth of the multi-valuedness of iterates of high-dimensional correspondences obtained as reductions of the QD-algorithm.

An integrable semi-discrete Degasperis-Procesi equation

NASA Astrophysics Data System (ADS)

Feng, Bao-Feng; Maruno, Ken-ichi; Ohta, Yasuhiro

2017-06-01

Based on our previous work on the Degasperis-Procesi equation (Feng et al J. Phys. A: Math. Theor. 46 045205) and the integrable semi-discrete analogue of its short wave limit (Feng et al J. Phys. A: Math. Theor. 48 135203), we derive an integrable semi-discrete Degasperis-Procesi equation by Hirota’s bilinear method. Furthermore, N-soliton solution to the semi-discrete Degasperis-Procesi equation is constructed. It is shown that both the proposed semi-discrete Degasperis-Procesi equation, and its N-soliton solution converge to ones of the original Degasperis-Procesi equation in the continuum limit.

The Kadomtsev{endash}Petviashvili equation as a source of integrable model equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maccari, A.

1996-12-01

A new integrable and nonlinear partial differential equation (PDE) in 2+1 dimensions is obtained, by an asymptotically exact reduction method based on Fourier expansion and spatiotemporal rescaling, from the Kadomtsev{endash}Petviashvili equation. The integrability property is explicitly demonstrated, by exhibiting the corresponding Lax pair, that is obtained by applying the reduction technique to the Lax pair of the Kadomtsev{endash}Petviashvili equation. This model equation is likely to be of applicative relevance, because it may be considered a consistent approximation of a large class of nonlinear evolution PDEs. {copyright} {ital 1996 American Institute of Physics.}